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Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
Göksu, Ömer
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2012
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Control of Wind Turbines
during Symmetrical and Asymmetrical Grid Faults
by
Ömer Göksu
Dissertation submitted to the Faculty of Engineering, Science & Medicine at Aalborg University
in partial fulfillment of the requirements for the degree of
Doctor of Philosophy in Electrical Engineering
Aalborg University
Department of Energy Technology
Aalborg, Denmark
December 2012
Aalborg University
Department of Energy Technology
Pontoppidanstraede 101
9220 Aalborg East
Denmark
Phone: +45 9940 9240
Fax: +45 9815 1411
Web: http://www.et.aau.dk
Copyright © Ömer Göksu, 2012
Printed in Denmark by UniPrint
ISBN 978-87-92846-18-1
ii
Abstract
As installed capacity of the wind power plants (WPPs) in power system of certain
countries increases, stability of the power system becomes more critical. In order to
sustain stable power system operation with high share of wind power, system operators
of some countries are enforcing more stringent grid code requirements, which are
targeting to make the WPPs operate in a closer manner to the conventional power
plants. Common to most of the grid codes, WPPs are required to stay connected during
short-circuit grid faults, and also inject reactive current in order to support the grid
voltage regulation. The uninterrupted operation of WPPs is required even when the grid
voltage drops down to zero; and the current injection requirement is defined as positive
sequence reactive current irrespective of the fault type; symmetrical or asymmetrical.
In this project, the response of full-scale converter type wind turbines (WTs), in an AC
connected WPP, is investigated and control algorithms are designed for minimum
disrupted operation and improved grid support, for both symmetrical and asymmetrical
grid faults. WTs’ response with conventional control algorithms is studied regarding
the impact on the WTs and the grid. Alternative control methods are proposed, which
are basically active and reactive current reference generation algorithms in positive
sequence and also in negative sequence.
It is observed that when WTs inject pure positive sequence reactive current in case of
asymmetrical faults in accordance with the grid code requirement, positive sequence
grid voltage is boosted, but negative sequence grid voltage is also boosted due to the
coupling. As a result higher overvoltages at the non-faulty phases occur. In this thesis
iii
an alternative injection method, where WTs are injecting both positive and negative
sequence currents, is given and compared with the conventional method in the sense of
grid support performance. Additionally, effect of the coupling between positive,
negative and zero sequences during asymmetrical faults, is investigated, which was not
considered in the wind power studies before.
It is shown that when reactive current injection is performed during severe symmetrical
faults, where the grid voltage is dropping down close to zero, the wind turbines can
lose the synchronism with the grid fundamental frequency, which potentially creates
risk of instability for the control. This Loss of Synchronism (LOS) situation is
investigated based on active and reactive current transfer limits which are derived first
time in this thesis, together with stability analysis of the grid synchronization of WTs.
Novel control algorithms are developed to generate necessary active and reactive
current references, which provide stable operation of the WTs and result in improved
grid support.
In summary, the response of the WTs to symmetrical and asymmetrical faults is
improved by means of the proposed control solutions, which provide compliance with
stringent grid codes, improved grid support with minimum disrupted operation, and a
WPP behavior in a closer manner to conventional power plants.
iv
Resumé på dansk
Som installeret kapacitet på vindkraftværkerne (WPPs) i et elsystem stiger, bliver
stabiliteten af elsystemet med høj andel af WPPs mere kritisk. For at opretholde en
stabil elsystem drift med høj andel af vindkraft, er operatørerne i lande håndhæve
strengere grid kodens krav, der er rettet mod at gøre WPPs fungerer på en lignende
måde som de konventionelle kraftværker. Fælles for de fleste af de netkrav er WPPs
forpligtet til at holde forbindelsen ved kortslutning netfejl, og også tilføre reaktiv strøm
for at støtte nettet spændingsregulering. Den uafbrudte drift af WPPs er nødvendig, selv
når netspændingen falder til nul, og den aktuelle injektion krav er defineret som positiv
sekvens reaktiv strøm uanset fejltype, symmetrisk eller asymmetrisk.
I dette projekt er respons i fuld Convertertype vindmøller (WTs), som står i et AC
tilsluttet WPP, undersøgt og reguleringsalgoritmer er designet til minimum forstyrret
drift og forbedret grid støtte, for både symmetriske og asymmetriske netfejl. WTs svar
med konventionelle reguleringsalgoritmer studeres for virkningerne på WTs'en og
gitteret. Alternative metoder er foreslået, som er dybest set aktive og reaktive
nuværende referencesatser algoritmer til generering i positiv rækkefølge og også i
negativ rækkefølge.
Det bemærkes, at når WTs indsprøjte rene positiv sekvens reaktiv strøm i tilfælde af
asymmetriske fejl i overensstemmelse med forsyningsnetkodeks krav, er positiv
sekvens netspændingen boostet, men negative sekvens af netspændingen stiger også på
grund af koblingen. Som følge højere overspændinger ved den ikke-defekte faser
forekommer. I denne afhandling en alternativ injektionsmetode, hvor WTs er injektion
v
både positive og negative sekvens strømme, er angivet og sammenlignet med den
konventionelle fremgangsmåde i betydningen bæringer ydeevne. Desuden effekt af
koblingen mellem positive, negative og nul sekvenser under asymmetriske fejl,
undersøges, som ikke blev behandlet i de vindenergiproducerende studier før.
Det vises, at når reaktiv strøm injektion udføres under kraftige symmetriske fejl, hvor
netspændingen falder ned tæt på nul, er vindmøller mister deres synkront med nettet
grundfrekvens, hvilket potentielt giver risiko for ustabilitet for kontrollen. Dette tab af
synkronisme (LOS) situation undersøges baseret på aktive og reaktive løbende
overførsler grænser, som er afledt første gang i denne afhandling, sammen med
stabilitet analyse af nettet synkronisering af WTs. Hidtil ukendte styrealgoritmer er
udviklet til at generere de nødvendige aktive og reaktive aktuelle referencer, som giver
stabil drift af WTs'en og resultere i forbedret bæringer.
Sammenfattende er respons WTs'en til symmetriske og asymmetriske fejl forbedret ved
hjælp af de foreslåede kontrolopløsninger, der giver overholdelse af strenge netkrav,
forbedret gitter støtte med mindst forstyrret driften og en WPP adfærd på en måde
svarende til konventionelle kraftværker .
vi
Acknowledgements
I acknowledge that this doctorate study was supported by the Aalborg UniversityVestas Wind Systems A/S partnership under Vestas Power Program.
I express my sincerest thanks to my main supervisor Remus Teodorescu, co-supervisor
Claus Leth Bak from Aalborg University (March 2012 – December 2012), cosupervisor Pedro Rodriguez from Technical University of Catalonia (October 2009 –
December 2011), and to Vestas Reference Group members; Florin Iov, Philip Carne
Kjær, and Lars Helle from Vestas Wind Systems A/S for their guidance, support,
encouragement, and valuable contributions throughout my doctorate study.
I would like to thank Tamas Kerekes for his help involved in experimental work in the
department laboratory. I wish to thank all employees in Vestas Technology R&D
Singapore, where I spent my four-month study abroad period with their kind
hospitability and where I was familiarized with wind turbine and wind power plant
control development in a professional R&D environment.
I would like to thank all my colleagues in Vestas Power Program and Department of
Energy Technology for their friendship throughout my doctorate study. I wish to thank
to the staff of Department of Energy Technology and Doctoral School of Engineering,
Science, and Medicine for their help throughout my doctorate study.
I want to dedicate this thesis to Kirse to express my gratefulness for her love making
life meaningful and to all my family and friends in Turkey for their generous and
continuous moral support.
vii
Table of Contents
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults i
Abstract.............................................................................................................. iii
Resumé på dansk ................................................................................................ v
Acknowledgements .......................................................................................... vii
Table of Contents............................................................................................. viii
List of Abbreviations ........................................................................................ xii
Chapter 1 ............................................................................................................ 1
Introduction ........................................................................................................ 1
1.1 Background............................................................................................ 1
1.1.1 Power System Response to Grid Faults .......................................... 2
1.1.2 Renewable Energy Sources in Power Systems ............................... 4
1.1.3 Weak Grid and Severe Fault Considerations .................................. 6
1.2 Overview of Grid Code Requirements .................................................. 9
1.3 Review of Grid Support by Wind Turbines during Faults .................. 12
1.4 Motivation and Objectives................................................................... 17
1.5 Scope of the thesis ............................................................................... 18
1.6 List of publications .............................................................................. 21
Chapter 2 .......................................................................................................... 23
Identified Problems during Grid Faults ............................................................ 23
2.1 Problems Observed during Asymmetrical Grid Faults ........................ 23
2.2 Loss of Synchronism during Symmetrical Grid Faults ....................... 26
viii
2.2.1 Simulation Case ............................................................................ 26
2.2.2 Fault Case-1: Loss of Synchronism – Frequency Fall .................. 28
2.2.3 Fault Case-2: Synchronized to 50Hz ............................................ 29
2.2.4 Fault Case-3: Loss of Synchronism – Frequency Rise ................. 30
2.2.5 Fault Cases with 0.1pu and 0.25pu PCC Voltages ....................... 30
2.2.6 PLL with Saturation and Anti-Windup Algorithm ....................... 34
2.2.7 Physical Understanding of LOS.................................................... 34
2.3 Conclusion ........................................................................................... 36
Chapter 3 .......................................................................................................... 38
Active and Reactive Current Transfer Limits................................................... 38
3.1 Active and Reactive Power Flow between Two Buses ....................... 38
3.1.1 Power Flow on a Line neglecting the Resistance ......................... 38
3.1.2 Power Flow on a Line considering the Resistance ....................... 41
3.2 Active and Reactive Current Flow between Two Buses ..................... 45
3.2.1 Current - Angle Characteristics .................................................... 45
3.2.2 Derivation of Active and Reactive Current Transfer Limits ......... 48
3.2.3 Summary of Current Transfer Limit Equations ............................ 59
3.3 Correlation of Current Transfer Limits with Wind Turbine Current
Injection ............................................................................................... 60
3.4 Two Operating Points Phenomenon .................................................... 65
3.5 Conclusion ........................................................................................... 67
Chapter 4 .......................................................................................................... 70
Analysis of Loss of Synchronism (LOS) during Symmetrical Faults .............. 70
4.1 Correlation of Observed LOS and Current Transfer Limits ................ 70
4.1.1 Response of WT to Non-transferrable Current Reference ............ 72
4.2 Large-Signal Stability Analysis of PLL during LOS .......................... 77
4.3 Experimental Verification of the Simulation Results .......................... 82
4.4 Small-Signal Stability Analysis within Transfer Limits...................... 88
ix
4.5 Conclusion ........................................................................................... 95
Chapter 5 .......................................................................................................... 98
Proposed Solutions for Loss of Synchronism ................................................... 98
5.1 State-of-the-Art Solutions.................................................................... 98
5.2 Impact of PLL Settings to LOS ......................................................... 106
5.3 Limited Current Injection during Severe Faults ................................ 108
5.4 X/R Based Active Current Injection .................................................. 110
5.4.1 X/R parameter uncertainty .......................................................... 114
5.5 PLL Frequency Based Current Injection ........................................... 117
5.5.1 Simulation Results of PLL Frequency Based Control Algorithm
..................................................................................................... 121
5.5.2 Experimental Results of PLL-Frequency Based Algorithm ....... 123
5.6 WPP Level Control............................................................................ 124
5.6.1 Active and Reactive Current Control at PCC ............................. 125
5.7 Minimum Active Power Requirement of Proposed Solutions........... 126
5.8 Summary of the Current Injection Schemes ...................................... 127
Chapter 6 ........................................................................................................ 132
Analysis of Asymmetrical Faults.................................................................... 132
6.1 Effects of Unbalance ......................................................................... 132
6.2 Analysis of the Problems Observed................................................... 134
6.2.1 Coupling Phenomenon during Asymmetrical Faults .................. 135
6.3 Conclusion ......................................................................................... 140
Chapter 7 ........................................................................................................ 142
Control Solutions for Asymmetrical Faults .................................................... 142
7.1 Dual-Sequence Current Injection Method ......................................... 142
7.2 Simulation Results ............................................................................. 144
7.3 Conclusion ......................................................................................... 150
Chapter 8 ........................................................................................................ 152
x
Multi-Turbine Case Studies ............................................................................ 152
8.1 LOS Problem for Multi-Turbine Case ............................................... 152
8.2 PLL Frequency Based Solution for Multi-Turbine Case................... 155
8.3 Interaction between Wind Turbines .................................................. 157
Chapter 9 ........................................................................................................ 160
Conclusions and Future Work ........................................................................ 160
9.1 Summary ........................................................................................... 160
9.2 Main contributions ............................................................................ 162
9.3 Future work ....................................................................................... 163
9.4 List of publications ............................................................................ 164
Bibliography ................................................................................................... 166
Appendix ........................................................................................................ 178
A1 Impact of Current Injection on the Grid Voltage during Symmetrical
Faults ................................................................................................. 178
A.2 WT Control Algorithms and Parameter Settings ................................ 187
Publications .................................................................................................... 189
[P1] published in Proceedings of OPTIM 2010 ............................................. 190
[P2] published in Proceedings of Wind Integration Workshop 2010 ............. 191
[P3] published in Proceedings of EPE Wind Chapter 2012 ........................... 192
[P4] published in Proceedings of IEEE PES GM 2012 .................................. 193
[P5] accepted for publication in IET Renewable Power Generation Journal 194
[P6] under review for publication in IEEE Transactions on Power Systems . 195
xi
List of Abbreviations
AC
Alternating current
CM
Conventional method
CPP
Conventional power plant
DC
Direct current
DFIG
Doubly fed induction generator
DLG
Double line-to-ground
DS
Dual-Sequence
ENTSO-E
European Network for Transmission System Operators for Electricity
FSCWT
Full-scale converter wind turbine
FRT
Fault ride-through
HVDC
High voltage direct current
LL
Line-to-line
LVRT
Low-voltage ride-through
NS
No-support
PCC
Point of common coupling
PI
Proportional and integral
PLL
Phase-locked loop
PR
Proportional resonant
PWM
Pulse-width modulation
RCI
Reactive current injection
RMS
Root-mean-square
SCC
Short-circuit capacity
SCR
Short-circuit ratio
SLG
Single line-to-ground
xii
STATCOM
Static reactive power compensator
TSO
Transmission system operator
VSC
Voltage source converter
WPP
Wind power plant
WT
Wind turbine
xiii
Chapter 1 Introduction
Chapter 1
Introduction
In this chapter, background of the thesis is given, as brief review of classical power
system stability, changes and challenges in the power system with installation of
renewable energy sources. The weak grid issue, which is gaining increasing
importance with high penetration of wind power plants in recent years, is discussed up
to an extent, together with severe grid faults. Progress of power system needs and
correspondingly developed grid codes are discussed. Details of the grid codes,
specifically fault requirements, including the dynamic response requirements, for wind
power plants are given, which will construct the basis for the problems identified and
solved in the following chapters of this thesis. The conventional and state-of-the-art
current injection methods by wind power installations are reviewed. The objectives,
scope and outline of the thesis are provided at the end.
1.1 Background
The electric power system, being continent wise interconnected, is considered to be the
largest controlled system in the world. Stability of the power system has been provided
successfully by means of implementation of hardware and software schemes on the
power system elements, such as generator controls, protection units, load management,
and also regulatory schemes applied by the responsible power system operators of
countries worldwide. Power system stability is classified as angle (frequency) and
voltage stability [1], where both are classified as large disturbance and small
disturbance and also as mid-term and long-term. Short-circuit grid faults, which are the
main focus of this thesis, are considered as large disturbances for both angle and
voltage stability of the power system.
1
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
1.1.1
Power System Response to Grid Faults
Reasons for grid faults are known to be environmental, such as lightning over a tower,
fall of a tree on an overhead line, or internal, such as short-circuits due to physical
wearing in power system units [2]. Grid faults can be classified as symmetrical (threephase) and asymmetrical (one, two-phase), where short-circuit to ground can also occur
for both types. Positive sequence grid voltage decreases for both symmetrical and
asymmetrical faults, whereas negative sequence (and zero sequence) voltage arises in
case of asymmetrical faults. As a general practice the “faulted period” ends when the
fault is cleared by disconnection of faulted part (line) of the network by means of
protection units (relays, circuit breakers) within few hundred milliseconds, and the
power system undergoes the “recovery period” taking few seconds back to normal
operation unless it is an unstable system [1].
It is known from power system theory that due to the low magnitude of (positive
sequence) grid voltage during a fault, rotational machines (generators and motors) can
exhibit angle instability, also depending on many factors such as prefault power level,
strength of the grid connections, fault clearing time [1]. Not only the rotational
machines but also other power system units (e.g. constant power loads) experience
problems due to the low grid voltage. The effect of low grid voltage is mitigated when
the grid voltage during fault is boosted, which inherently occurs with high fault
currents flowing from nearby synchronous generators of conventional power plants
(CPP). Hence, in general the grid voltage during a fault is observed to be higher if there
exists CPPs nearby the fault and/or the impedance of the network connections is low,
which together implies a high Short-Circuit Capacity (SCC) and strong grid. Hence, as
a general conclusion, stability of the grid is improved when the grid voltage is boosted
towards rated value during fault.
As stated above, during asymmetrical faults negative (and zero) sequence voltages arise
in the grid, whereas the drop of positive sequence voltage is not as severe as the
symmetrical faults [1]. Therefore, risk of instability during asymmetrical faults is quite
low compared to symmetrical faults. However, high zero sequence and negative
sequence voltages cause overvoltages in the non-faulted phases; and also the negative
sequence voltage causes problems like power (and torque) oscillations in the power
2
Chapter 1 Introduction
system elements like generators, motors, and grid-connected converters (e.g.
distributed generation units, adjustable speed drives). The synchronous generators of
CPPs have the capacity for flow of negative sequence currents, which in turn helps to
mitigate the negative sequence voltage, whereas the magnitude of zero sequence
voltage is mainly dependent on the neutral grounding of the system, mainly through
transformers [3]. Effect of asymmetrical faults is assessed in detail in the related parts
of the thesis. As a general conclusion, the impact of asymmetrical faults is mitigated
when the grid positive sequence voltage is boosted towards rated; and negative (and
zero) sequence voltages are attenuated towards zero during fault.
Following the clearance of the fault via disconnection of the faulted part (line) of the
network by protection units, power system undergoes the recovery period (post-fault),
where the power system recovers back to normal operation [1]. The synchronous
generators of CPPs can stay connected during faults and can recover to normal
operation after fault unless they are disconnected from the grid due to disconnection of
the faulted part. Compared to the prefault conditions, after the fault the system
continues with a new equilibrium point with some part of the grid disconnected. The
balance for generation and consumption of active and reactive power after fault is
crucially important considering the frequency and voltage stability. Additionally,
during the recovery period, where the grid voltage is rising back to rated, all the power
system elements experience transients, such as re-magnetization of the asynchronous
motor loads, restoration of active power consumption. Hence, it is crucial that the
power plants stay connected (do not disconnect) during a fault and properly restore
back to stable operation. In summary, in case of a fault (which is assumed to be cleared
securely by protection units), power system stability requires that;
o
power plants stay connected to guarantee power balance after the fault,
o
positive sequence grid voltage is boosted towards rated value to mitigate impact
of low voltage during fault,
o
negative sequence voltage is attenuated towards zero (phase voltages are
balanced) to mitigate unbalance effects during fault,
o
active and reactive power generation is ramped-up properly during the recovery
period to provide restoration of the power system to a new stable point.
3
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
1.1.2
Renewable Energy Sources in Power Systems
As the price of the fossil fuels is rising and risk for their availability is appearing
worldwide; and above all as the environmental problems and climate change due to
excessive use of fossil fuels are being considered seriously by countries, renewable
energy, especially the wind energy is becoming more and more important. Hence, more
renewable energy sources, especially the wind power plants are being installed in
power systems [4], both as new additional units and as replacement of CPPs. As
discussed above, CPPs, which are based on synchronous generators directly connected
to the grid, have inherent capabilities to provide stable power system operation and
participate in the balancing act. The replacement of CPPs with WPPs has influence on
the security of the supply since the WPPs do not exactly replace the functional behavior
of the CPPs, due to the specific characteristics of the WPPs [5] – [7]. In conjunction
with progress of available technology and parallel to the requirements of market and
grid, newly installed WPPs are based on the modern wind turbine type of variable
speed wind turbines, which can be considered as two types as Full-Scale Converter
Wind Turbines (FSCWT) and Doubly-Fed Induction Generator (DFIG) wind turbines
[8] – [10]. The variable speed wind turbines have the common characteristics that the
active and reactive power (current) are controlled as to be within rated limits and the
generation is non-synchronous as machines are connected to the grid through power
electronics. Most importantly, disconnection of WPPs in case of grid faults is found to
be a huge risk for the power system considering the active and reactive power balance
during recovery period of the fault and the balance after the fault [11], [12]. A generic
WPP structure is given in figure 1.1, which is the basis within this thesis. As seen in
figure 1.1, in a generic WPP, wind turbines have voltage and current feedback at the
low-voltage side of their transformers, where they perform controlled active and
reactive current (and power) injection; the WPP employs voltage and current
measurements, which can be utilized for WPP control actions, at the Point of Common
Coupling (PCC), where it is connected to the AC grid; and communication between
WPP controller and WTs exist [9], [13].
4
Chapter 1 Introduction
Figure 1.1 Generic WPP system based on FSCWTs.
In order to provide stable power system operation with increasing capacity of WPPs,
the countries, especially the ones with high wind penetration, have been applying
regulations for WPPs as grid codes for wind power integration, with extent being
increased continuously [14] – [21]. In recent grid codes, WPPs are required even to
contribute to frequency and voltage stability of the power system, via responding with
synthetic inertias, primary frequency control, voltage regulation and power oscillation
damping functions [21]. Regarding the faults, common to most of the grid codes as a
fundamental requirement, WPPs are required to stay connected (not to be disconnected)
in case of grid faults, in order to sustain active and reactive power balance after the
fault. This action of staying connected, which is called as Fault Ride-Through (FRT), is
required even when the grid voltage drops down to zero in certain grid codes [17], [21].
In addition to FRT requirement, WPPs are required to support the grid voltage via
injecting reactive currents during the fault, including both the faulted and recovery
period, in order to regulate the grid voltage towards rated value. This action of injecting
reactive current during fault, which is called as Reactive Current Injection (RCI), has
magnitude limited to rated current of wind turbines in accordance with their
technology. The WPPs are required to inject reactive current during faults, which can
be considered as a voltage control action, in order to regulate the grid voltage during
fault to improve angle stability of the power system [22], and to support the grid during
recovery period of the fault to avoid any voltage collapse event [23]. Details of the grid
5
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
code fault response requirements are given in the following sections. In summary, with
the grid codes, WPPs are aimed to behave in a similar manner to CPPs.
As stated above, WPPs are not having the same functional capabilities and capacities as
CPPs considering active and reactive power generation and control. Regarding the
faults, current injection from WPPs is limited by their rated values (e.g. 1pu) or can be
slightly higher for short-term (e.g. 1.25pu), which is quite low compared to high (25pu) fault currents from CPPs. Additionally, when the wind resources are far from
generation and consumption centers, the WPPs are connected with long lines and the
power system is expanded with long connections. As a result of these and replacement
of CPPs with WPPs, the grid with high penetration of WPPs becomes weak grid. In
conclusion, installation of WPPs to power system is a challenge for providing the
power system stability.
1.1.3
Weak Grid and Severe Fault Considerations
With the increasing share of renewable energy sources and also due to other reasons
discussed below, power systems are becoming less strong, i.e. weak grid. Strength of a
grid, or specifically of a bus in the grid, can be represented by its Short-Circuit
Capacity (SCC), which is related to the amount of current flowing to a solid fault at this
bus [24]. When grid seen from a bus is represented by its Thevenin equivalent as seen
in figure 1.2-(b), the SCC is calculated as below;
SCC=
Vgrid
Z grid
(1.1)
Hence, lower the Thevenin equivalent impedance, stronger the grid is. The ShortCircuit Ratio (SCR) of a bus, where a WPP is connected, is ratio of the SCC at the
related bus to the rating of the WPP(s) connected at this bus;
SCR=
SCC
S W PP(s)
The following is a definition of the strength of an ac system in [25]:
o
strong system, if the SCR of the ac system is greater than 3.0.
o
weak system, if the SCR of the ac system is between 2.0 and 3.0.
o
very weak system, if the SCR of the ac system is lower than 2.0.
6
(1.2)
Chapter 1 Introduction
In German VDN grid code [17], it is stated that the initial SCC present at the grid
connection point and also after fault clearance shall be greater than 6 times the total
amount of nominal active powers of all wind energy plants connected at the related
connection point; implies that a strong network with minimum SCR of 6 (Zgrid smaller
than 0.17pu) is guaranteed by the related Transmission System Operators (TSO) for the
connection of the WPP. In Danish grid code [20], SCR is suggested to be used as 10
within system studies, implying a very strong system, which is possible in Denmark.
However, in certain countries and in certain cases and with the increasing installation
of renewables, SCR can go lower [26] – [32], even below 2. A grid becomes weak grid;
o
if network has high impedance lines, and/or not connected to strong neighboring
networks, expanded to a large area with long lines, then the related network has
low SCC overall (weak grid);
o
if the power system becomes highly renewables based generation replacing the
CPPs as seen in figure 1.2-(a), then the SCC at all buses gets lower (weak grid),
o
if network has poor lines and/or the bus, where WPP is connected, is located far
away, then the related bus has low SCC (weak bus),
o
if rich wind resources are further away from centers, then there is need for a
connection line which would result lower SCC at PCC of WPP (weak bus),
o
additionally, if the WPP has high internal impedance (transformers and collector
grid), SCC becomes even lower at WT terminals (for a grid fault external WPP).
Severity of a fault is highly related with the duration of the fault and the voltage drop
during fault [1]. Voltage drop during a fault is mainly related to fault impedance and
strength of the grid. In this thesis, a “severe fault” for a WPP means a fault, where the
voltage at the PCC of the WPP is measured lower than a certain value (e.g. 20%); and a
“non-severe fault” is a fault with voltage higher than that certain value. A severe fault
for a WPP occurs due to some or all of the below cases;
o
if fault location is near to WPP (e.g. at PCC or at buses 1 to 4 in figure 1.2-(a))
o
if the fault impedance is very low (i.e. solid fault)
o
if the bus, where the WPP is connected, is a weak bus (low SCC); which means
that the WPP is located far from the central generation and/or it is a weak grid.
7
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
Fig. 1.2 (a) Low SCR connection with representative SCR values, (b) Thevenin
equivalent of main grid.
Fault impedance magnitude and characteristics has not been paid sufficient attention in
previous wind power studies, though it is a very important factor affecting the severity
of a fault. In previous wind power fault studies, which are reviewed in the following
sections, the fault impedance magnitude is adjusted to obtain a remaining voltage
convenient for the scope of the related study. In practical, a symmetrical solid fault at
PCC or nearby can result in a very low (e.g. 2%) voltage at the faulted point, even for a
strong system with low grid impedance. Such low voltage occurrences are also covered
within grid code requirements, which are detailed below.
8
Chapter 1 Introduction
1.2 Overview of Grid Code Requirements
In this section, in relation to the main scope of this thesis, grid codes are reviewed
focusing on the fault response requirements for WPPs and wind turbines. Requirements
from two exemplary grid codes are reviewed with details; namely the German VDN
grid code [17], which is one of the most established grid codes in the world inspiring
the followers, and the recently published European Network for Transmission System
Operators for Electricity (ENTSO-E) grid code, which is prepared by a consortium to
be the common grid code frame for all European countries [21].
The German VDN grid code [17], covering WPPs connected to transmission and subtransmission voltage levels, is introducing the FRT and RCI requirements for the
WPPS. Regarding the FRT requirements, the WPPs are expected to stay connected
even when the grid voltage drops down to zero, as seen in figure 1.3-(a). The RCI
requirement is requested as a proportional voltage control scheme, where the gain can
be adjustable between 0 and 10 and with a deadband applied to the voltage deviation,
as seen in figure 1.3-(b). The reactive current during fault is requested as additional to
the prefault reactive current, where the total reactive current magnitude is limited to the
rated (1pu) value. As a result, with a moderately selected gain of 2, which is the default
value [17], 1pu reactive current is injected when the voltage drops below 50%. Active
current is allowed to be decreased in order to keep the total current within capability of
the wind turbine. Additionally, dynamics of step response for the reactive current is
defined as seen in figure 1.3-(c). It is requested that the reactive current rise time is
30msec and settles within a tolerance of -10%/+20% within 60msec, following the
occurrence of the fault. In [17], the FRT requirement is defined for the PCC of the
WPP; whereas the RCI requirement is stated to be realized at the wind turbine level at
low-voltage side of the wind turbine transformer, but also verification at PCC level is
encouraged in order to allow innovative WPP solutions.
9
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
Fig. 1.3 German VDN grid code fault response requirements; (a) FRT, (b) RCI, (c) RCI
step response requirements [17].
Regarding the recovery period of the fault, the RCI injection based on voltage drop is
required to be continued for 500 milliseconds following the clearance of the fault, and
active power ramp-up requirement is set as increase of active power between 10% and
20% of the nominal value per second.
In summary, German VDN grid code is requesting the WPPs to realize a proportional
voltage control scheme at the PCC point and behave in a similar manner to CPPs
during faults. There are similar requirements in many of the grid codes from other
countries and TSOs [14] - [15].
Regarding the fault response requirements, ENTSO-E code is similar to the German
VDN grid code, with few differences. As seen in figure 1.4, the FRT requirement of
ENTSO-E is almost the same as VDN’s, requiring the transmission level connected
WPPs to stay connected even when the grid voltage drops down to zero. The dynamic
step response requirement for the RCI is more stringent in ENTSO-E than in VDN. It is
stated that the WPP or the individual WTs “shall be capable of providing at least 2/3 of
10
Chapter 1 Introduction
the additional reactive current within a time period specified by the relevant TSO,
which shall not be less than 10 milliseconds and the target value of this additional
reactive current shall be reached with an accuracy of 10% within 60 milliseconds from
the moment the voltage deviation has occurred” [21].
Fig. 1.4 ENTSO-E grid code FRT requirements (a) <110kV, (b) •110kV [21].
Regarding the asymmetrical faults, the maximum reactive current requirement in VDN
grid code [17] is set to be 40% of the rated, much lower than the 100% for symmetrical
faults; however any explanation is not provided. Additionally in Spanish grid code
[18], [19] only informative statement is given about the flow of negative sequence
currents. In ENTSO-E grid code, FRT response during asymmetrical faults and current
injection is stated to be defined by agreements between system and plant operators. It
can be commented that asymmetrical faults are not targeted exclusively within grid
codes, likely due to the reason that asymmetrical faults are not severe faults and do not
carry high risk for power system stability [33]. However, in the transmission system of
power systems, asymmetrical faults are observed more frequently with occurrences as
single line-to-ground (SLG) faults with 70%, line-to-line (LL) faults with 15%, double
line-to-ground (DLG) faults with 10%, than symmetrical faults with only 5%
occurrence [34]. Considering that asymmetrical faults are occurring more frequently
than symmetrical faults, specific requirements for asymmetrical faults can be more
beneficial.
11
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
In summary, the existing grid codes are requiring the WPPs to stay connected and
inject positive sequence reactive currents proportional to the voltage deviation,
irrespective of the fault type is symmetrical or asymmetrical; and even for severe faults
with grid voltage close to zero. In this thesis, two specific problems, which are
explored in case of reactive current injection during severe symmetrical faults, and pure
positive sequence reactive current injection during asymmetrical faults, are investigated
and solved by proposed methods in the following chapters.
1.3 Review of Grid Support by Wind Turbines during Faults
In accordance with the grid code requirements, modern wind turbines are equipped
with the capability to stay connected and to support the grid during faults [13]. The
conventional method for current injection during faults, complying with the RCI
requirement, is given in figure 1.5 below. In the figure, Igcm is the grid code maximum
reactive current value, which is required as the rated current (1pu) value in general.
As seen in figure 1.5, which is employed as the conventional control method during
faults, active and reactive current references are generated based on the voltage at the
feedback terminals, and DC link voltage regulation, respectively. During a low voltage
fault, the active power that can be injected to the grid decreases due to low grid voltage.
Additionally, since priority is given to reactive current injection in order to fulfill the
grid code requirement, low or zero capacity remains for the active current, depending
on the current capability of the wind turbine. Due to these reasons, the excess active
power flowing from the machine side converter, which cannot be injected to the grid, is
dissipated on the chopper resistance. In figure 1.5, block-1 generates the reactive
current reference based on the grid code profile and the voltage measured at the
terminals. The consideration for prefault reactive current value is omitted for simplicity
in figure 1.5. In block-3, the remaining current capacity (Iactive-limit) is calculated based
on the current capability of the wind turbine grid side converter (Icapable) and the
reactive current reference. Then, the active current reference is limited to be less than
limit (Iactive-limit) value.
Two representative cases for active and reactive currents are shown on the grid code
reactive current profile in figure 1.6. It is important to note that, the grid code
12
Chapter 1 Introduction
maximum reactive current requirement value (Igcm) can be either equal to or smaller
than the wind turbine current capability (Icapable). Wind turbine grid-side converter can
have higher capacity (e.g. 1.25pu) or can be overloaded for a short-term during fault;
hence as in figure 1.6-(b) there can be remaining capacity for active current even when
the reactive current reference reaches grid code maximum reactive current value. The
active current can be injected as any value in the scanned areas, depending on the
active power flow from machine-side converter.
I*reactive
I*reactive
2
2
*
IactiveͲlimit = Icapable ͲIreactive
I*active
I**
active d IactiveͲlimit
I**
active
Fig. 1.5. Conventional method for current reference generation during fault.
Fig. 1.6. Current references with conventional method (a) Icapable = Igcm (b) Icapable > Igcm.
In accordance with the grid code requirements and operational requirements, modern
wind turbines are designed to have the capability of injecting active and reactive
13
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
current (power) independently, i.e. as vector current control with the required dynamic
bandwidth. In order to realize active and reactive current control at the wind turbine
terminals, well-established current control and grid synchronization methods are
utilized [35] – [43]. In general, current control can be performed in two ways; as a
double synchronous frame regulator based on PI compensator and as a stationary frame
regulator based on a PR compensator. Both control structures employ grid
synchronization schemes as Phase Locked-Loop (PLL) or Frequency Locked-Loop
(FLL).
The current regulator and grid synchronization algorithms are designed and tuned to
provide the necessary dynamic response requirements. As a general approach, current
regulation bandwidth, which is also highly dependent on sampling and switching
frequency of the wind turbine converter, is designed to reach a time constant of 0.5ms –
5ms [44], which even complies with the stringent 10msec rise time requirement of
ENTSO-E grid code. The grid synchronization is tuned to have a time constant larger
than fundamental period (e.g. 20msec) to track the grid angle with necessary dynamic
response and to realize high performance vector current control. Details of the current
regulator and grid synchronization functions and parameter settings in this thesis are
given throughout the related parts of the thesis and also in appendix.
As the fundamental requirement common to most of the grid codes [14] – [21], FRT
and RCI requirements has drawn great attention both by academia and wind power
industry. Several research studies on requirement, impact, implementation of FRT and
RCI have been accomplished [45]-[73].
Regarding FRT of wind turbines during symmetrical faults [45] – [56], research has
been concentrated on two main topics; impact of faults on wind turbine stability (e.g.
dc link voltage control, generator speed, current control) and impact of wind turbines’
fault response on the grid (stability of the power system and nearby units). In [45],
transient oscillations occurring in the dc link voltage and generator speed of a fullconverter type wind turbine is proposed to be solved. In [46] – [48], rise of dc link
voltage during symmetrical faults due to incoming active power from generator side is
suggested to be solved by use of chopper, additionally blocking due to high dc link
voltage and restart of converters is studied in [47]. Impact of wind turbines’ fault
14
Chapter 1 Introduction
behavior on power system stability is thoroughly studied in [49] – [53]. Response of an
induction motor load nearby PCC is compared for cases with and without RCI support
from wind turbines, and improvement obtained is given in [49]. Transient stability of
part of the network nearby a WPP is investigated and RCI schemes to improve angle
stability of nearby synchronous generators are proposed in [50]. In [53], advanced
control methods to control current of a converter during grid faults to avoid over
current events are proposed. In [54], interaction between wind turbine fault response
and structural behavior of tower and blade oscillations is investigated. In [55], wind
turbines connected as a WPP are investigated for their stability against resonance
within the collector network, considering the shunt capacitances of the cables; and a
method is proposed to be implemented for each wind turbine to avoid resonance due to
interaction of the closed loop current control of wind turbine grid side converter.
Hence, the previous symmetrical fault studies are either focusing on wind turbine
stability in the sense of dc link and generator side; or impact of wind turbine response
on the grid side. Additionally, within these fault studies, the grid voltage is analyzed to
drop down to 10% of rated but not lower; despite the grid codes [14], [17], [21] have
requirements for zero grid voltage. In practical, during a symmetrical solid fault near
PCC of a WPP, voltage can drop down close to zero for the WPP, which is a case not
comprehensively covered in the previous studies. In this thesis, a previously
underestimated and omitted phenomenon of converter (angle) instability problem as
Loss of Synchronism (LOS) is explored, investigated and solved, which is specifically
encountered during RCI to very low voltage (for example less than 10% of rated) fault
cases. The mentioned problem with very low voltage faults is handled only in [56],
which targets only highly active current injection during fault, as will be assessed in
detail in the related chapter five. In [57], simulation and test results are given for a fullconverter wind turbine, for a zero voltage fault, however fault is created at the turbine
terminals, not at PCC of the WPP, and detailed information about active and reactive
current (power) injection scheme is not provided.
Regarding the asymmetrical faults, considerable amount of research is conducted for
analysis and control development for wind turbines’ response during asymmetrical
faults. Main focus topics have been mitigation of the impact of asymmetrical faults on
15
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
the wind turbines. For instance in [58] – [65], control schemes are developed to
mitigate twice the grid frequency oscillations occurring during asymmetrical faults. In
[66], oscillations are damped also considering the power loss on the filter impedance.
Classifications for unbalanced voltage profiles observed at the wind turbines terminals
is provided in [67], whereas proposals for asymmetrical test procedures are given in
[68]. From the grid point of view, the approach of reducing the negative sequence
voltage (balancing the grid voltages) via injecting underexcited (inductive) reactive
currents by wind turbines is studied in [69] – [72], and as a Statcom capability in [72].
However, most of the previous asymmetrical fault studies are focusing on control via
wind turbine point of view, not many are considering the impact of wind turbines’
response on the power system. Only in [73], overvoltage problem at the non-faulty
phases is handled. However, with increasing share of wind power, a need for
assessment of wind turbines impact on the power system during asymmetrical faults
arises. In this thesis, impact of wind turbines’ reactive current injection on the power
system is investigated comparing conventional method of positive sequence reactive
current injection with alternative methods of injecting both positive and negative
sequence reactive currents. The physical phenomenon of coupling between positive,
negative and zero sequence networks during asymmetrical faults, which has not been
considered in the previous studies, is explored and taken into account in wind turbine
control.
In summary, this thesis is contributing to the fault literature with the two focus areas
below;
o
Stability of full-converter wind turbines during current injection to severe
symmetrical grid faults (e.g. 5% voltage at PCC); exploring the Loss of
Synchronism (LOS) problem and proposing novel solutions to provide wind
turbine stability.
o
Impact of reactive current injection of full-converter wind turbines on the power
system voltages during asymmetrical grid faults, which are occurring at or near to
PCC of a WPP.
16
Chapter 1 Introduction
1.4 Motivation and Objectives
Main motivation of this project is to develop new control strategies for wind turbines’
fault response that can enable increased wind power penetration in existing power
systems without degrading the stability. As discussed above and in literature, risks for
security of a stable power system arise with high penetration of wind power, mainly
due to distinct characteristics of wind power installations. In this project the purpose of
making the WPPs behave similar to CPPs is targeted, focusing on the response of
WPPs during symmetrical and asymmetrical grid faults. In the FRT and RCI
requirements of certain grid codes [14], WPPs are expected to stay connected and inject
reactive current during symmetrical faults even when the grid voltage drops down to
zero. WPPs are also required to stay connected and inject positive sequence reactive
current during asymmetrical grid faults, which in turn helps to boost the positive
sequence grid voltage.
First, it is shown that when reactive current is injected during severe symmetrical faults
with grid voltage close to zero (e.g. 5% of rated), wind turbines lose their synchronism
with the fundamental frequency (e.g. 50Hz) of the main grid, named as Loss of
Synchronism (LOS) problem. In this thesis the LOS problem is explored in detail and
novel methods are developed to provide wind turbine stability and in turn helping the
power system stability during severe symmetrical faults.
Secondly, it is shown that when pure positive sequence reactive current is injected
during asymmetrical grid faults, positive sequence grid voltage is boosted, but negative
and zero sequence voltages are also boosted due to coupling between sequences. As a
result, higher phase overvoltages at the non-faulty phases and higher negative sequence
voltages in the grid are observed. In this thesis detailed analysis of asymmetrical faults
and improved grid support is obtained by means of an alternative injection method.
Focusing on two specific cases, which have not been studied thoroughly before, the
main objectives are set as below;
o
Provision of reactive current injection during severe symmetrical grid faults
even when the grid voltage drops down close to zero, such that the wind
17
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
turbines are not disconnected and continues stable operation during fault, the
grid voltage is supported; and the wind turbines can continue their operation
without interruption.
o
Provision of positive and also negative sequence current injection during
asymmetrical grid faults, the positive sequence grid voltage is boosted,
negative sequence grid voltage is attenuated; and the grid voltage support is
improved compared to the conventional method.
1.5 Scope of the thesis
As stated in the objectives, the response of WPPs during symmetrical and asymmetrical
grid faults is investigated and control solutions are developed within this thesis. Two
specific cases are investigated and control solutions are developed for problems
occurring during these cases. For both of the cases only the faulted period (from the
instant of the fault occurrence till the clearance) of the fault is considered, excluding the
recovery period. Any disturbance caused by disconnection of any (faulted) line in
conjunction with the fault clearance is kept out of scope.
The WPP under investigation is an AC connected WPP, which can be onshore and
offshore as well, and composed of several FSCWTs, with several MW (e.g. 5MW)
ratings. Being not limited; the WPP rating is chosen to be around few hundred
megawatts (100MW) and connected to sub-transmission (e.g. 100kV) or transmission
(e.g. 230kV) levels. However, the analysis and developed solutions can be applied to
wind turbines singly connected to medium voltage (e.g. 30kV) level. The WPP under
scope is not considered to have any units connected to its PCC point, such as Statcom
or cap banks.
The studied asymmetrical faults are shunt (parallel) type asymmetrical faults, which are
commonly observed in the transmission system [34], as; single line-to-ground (SLG),
double line-to-ground (DLG), line-to-line (LL). Rarely observed series (open circuit)
asymmetrical faults are not considered within scope.
18
Chapter 1 Introduction
Mathematical analysis is accomplished based on the Thevenin equivalent of the grid at
the connection point, whereas a connection line (e.g. overhead line or underground
cable) is included with its PI models. The WPP in mathematical analysis is an
aggregated WPP structure, as a single wind turbine with rating equal to the rating of the
WPP, and with equivalent collector network impedance [74] – [76].
Within the mathematical analysis, simulation models, and analysis of the response of
the wind turbine during faults, the rotor aerodynamics of the FSCWT, the generator
side converter, the generator itself and the dc link are represented as a constant dc
voltage source since these parts have low bandwidth compared to the short duration of
the faults [77], and additionally since the focus is given to grid impact and control of
wind turbine current injection during faults. Additionally, since the scope is not having
power electronics aspect, the switches in the grid-side converter of the wind turbine are
neglected and the converter is modeled using ideal controlled voltage sources [78].
The outline of the thesis is as follows;
Chapter 1: Introduction, presents background of the project, including impact of wind
power plants on power system stability during faults, and correspondingly developed
grid code requirements for wind power plants; also provides an overview of wind
turbine control during faults and the conventional method for current reference
generation during faults. The chapter is concluded with motivation, objectives and
scope of the project.
Chapter 2: Identified Problems during Grid Faults, provides detailed representation
of the problems encountered when the conventional method of current reference
generation is utilized during grid faults, with simulation results of several cases. The
phase overvoltage and coupling problems observed during asymmetrical faults and
Loss of Synchronism (LOS) problem during severe symmetrical faults are introduced.
Chapter 3: Active and Reactive Current Transfer Limits, is derivation of current
transfer limits between two buses, which is a basic but fundamental theoretical
reference for active and reactive current injection from wind turbines.
Chapter 4: Analysis of Loss of Synchronism (LOS) during Symmetrical Faults,
explores the source of the LOS problem observed during severe symmetrical faults,
19
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
showing the relation with the active and reactive current transfer limits. Results and
stability limits derived from large-signal stability analysis of the grid synchronization
scheme (PLL) are also given, which shows consistency with the current transfer limits
derived in chapter 3. In this chapter, simulation results of observed LOS problem are
verified with experimental investigation on a grid-connected converter. Small-signal
stability analysis of the PLL is also accomplished, which serves for development of
control algorithms in the next chapter.
Chapter 5: Proposed Solutions for Loss of Synchronism during Symmetrical Faults,
starts with review and assessment of state-of-the-art solutions for LOS problem, and
continues with detailed presentation of solutions proposed in this thesis. The proposed
novel PLL frequency based current reference generation algorithm is verified with
simulation and experimental investigations. At the end, comparison of current reference
generation schemes from point of view of wind turbines’ fault ride-through and
reactive current injection requirements is done.
Chapter 6: Analysis of Asymmetrical Faults, explains the cause of identified problems
during asymmetrical faults, which were shown in first part of chapter 2. Additionally,
effects of unbalance both for short-term and long-term are summarized as a reference
for negative sequence current injection.
Chapter 7: Control Solutions for Asymmetrical Faults, reviews control methods
during asymmetrical faults, and presents the alternative dual-sequence current injection
method, which is shown to yield improved grid support with simulation results.
Chapter 8: Multi-Turbine Case with Proposed Method, involves application of
proposed control solution as implementation for multi-turbines.
Chapter 9: Conclusion, summarizes the thesis and lists the main contributions and
future work.
Appendix includes analysis for impact of WPPs’ support on the grid voltage,
emphasizing the importance of fault impedance characteristics and parameters used
within wind turbine control algorithms.
20
Chapter 1 Introduction
1.6 List of publications
Publication 1 reviews the grid code requirements, which are given in chapter 1.
Publication 2 is incorporated in chapter 1 as a general state-of-the-art of generic wind
turbine control. Publication 4, is the short-circuit calculation tool utilized to analyze
asymmetrical faults in chapter 6. Publication 5 includes asymmetrical fault studies
covered mainly in chapter 2, 6 and 7. Publication 6 covers the LOS problem and the
proposed PLL frequency based solution placed in chapters 2, 3, 4 and 5.
P1. Mufit Altin, Ömer Göksu, Remus Teodorescu, Pedro Rodriguez, Birgitte BakJensen, and Lars Helle, “Overview of recent grid codes for wind power
integration,” International Conference on Optimization of Electrical and Electronic
Equipments, Romania, May 2010
P2. Ömer Göksu, Remus Teodorescu, Pedro Rodriguez, and Lars Helle, “A Review of
the State of the Art in Control of Variable-Speed Wind Turbines,” 9th International
Workshop on Large-Scale Integration of Wind Power into Power systems, Quebec,
Canada, October 2010
P3. Andrzej Adamczyk, Mufit Altin, Ömer Göksu, Remus Teodorescu, and Florin Iov,
“Generic 12-Bus Test System for Wind Power Integration Studies,” EPE Joint
Wind Energy and T&D Chapters Seminar, Aalborg, Denmark, June 2012
P4. Ömer Göksu, Remus Teodorescu, Birgitte Bak-Jensen, Florin Iov, and Philip Kjær,
"An Iterative Approach for Symmetrical and Asymmetrical Short-Circuit
Calculations with Converter-Based Connected Renewable Energy Sources.
Application to Wind Power," IEEE Power & Energy Society General Meeting, San
Diego, USA, July 2012
P5. Ömer Göksu, Remus Teodorescu, Claus Leth Bak, Florin Iov, and Philip Kjær,
"Impact of Wind Power Plant Reactive Current Injection during Asymmetrical
Grid Faults,” IET Journal of Renewable Power Generation, accepted.
P6. Ömer Göksu, Remus Teodorescu, Claus Leth Bak, Florin Iov, and Philip Kjær,
"Instability of Wind Turbine Converters during Current Injection to Low Voltage
Grid Faults and PLL Frequency Based Stability Solution,” IEEE Transactions on
Power Systems, under review.
21
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
22
Chapter 2 Identified Problems during Grid Faults
Chapter 2
Identified Problems during Grid Faults
In this chapter, identified problems, when conventional method for current reference
generation is employed during asymmetrical and symmetrical grid faults, are given. It
is shown that during asymmetrical grid faults, if the wind power plant is injecting pure
positive sequence reactive current, the positive sequence voltage is boosted as desired;
but negative and non-faulted phase voltages are also boosted. The loss of synchronism
(LOS) problem, which is observed during severe symmetrical faults, is described and
shown with simulations. It is shown that, depending on the wind turbine current
injection, i.e. active and reactive current magnitudes, and the voltage magnitude at the
faulted bus, the wind turbines can lose their synchronism with the fundamental
frequency (e.g. 50Hz) of the grid.
2.1 Problems Observed during Asymmetrical Grid Faults
As a conventional method (CM) complying with the grid code requirement of reactive
current injection, modern WTs are injecting pure positive sequence (symmetrical)
currents boosting positive sequence voltage. The magnitude of the reactive current is
limited to current capacity (e.g. 1pu) of the wind turbine, whereas the conventional
power plants (CPP) can inject higher values (e.g. 3pu). Positive sequence reactive
current injection by WPPs helps the grid voltage via boosting the positive sequence
voltage, in case of low voltage faults. However, as will be shown below, when this
conventional method is employed in case of asymmetrical faults, which is injection of
pure positive sequence current and keeping negative sequence current as zero, all three
phases, including the non-faulty phase(s) are boosted. Since negative sequence current
injection of WPP is kept as zero, which means that WPP behaves as open circuit in
23
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
negative sequence, negative sequence voltage is not attenuated and propagates towards
the WPP. Though only positive sequence current is injected, it is observed that negative
and zero sequence voltages are additionally boosted at the fault point, due to coupling.
Consequently, higher negative sequence voltage and higher phase overvoltages are
observed towards WPP.
Comparison of three cases are given in figure 2.1; in the first case response of a CPP
based on synchronous generators to a SLG fault (at phase-“a”) is shown, in the second
case CPP is supplanted by a WPP, which is injecting zero current during the fault, in
the third case WPP is injecting pure positive sequence current in accordance with the
CM. The voltage magnitudes and phase angles are obtained from time-domain
simulations. In both cases power plants are connected radially to the main grid via
20km long overhead lines. As observed from figure 2.1-(a) and (c), in positive
sequence both power plants are boosting the positive sequence voltage by means of
supplying fault currents. As expected, CPP can boost the positive sequence voltage
more than the WPP, due to high current capability of CPP.
Comparing the phase voltages in figure 2.1(b) and 2.1-(c), it is observed that with the
use of CM, which is injecting pure positive sequence currents, non-faulty phases (“b”
and “c”) are boosted from 1.08pu to 1.13pu at the faulted point, and from 0.95pu to
1.04pu at PCC, unnecessarily above rated. Additionally, even though only positive
sequence reactive current is injected, negative sequence voltage at the faulted bus
increases from 0.28pu to 0.30pu due to the coupling. Hence, high negative sequence
voltages and phase overvoltages are observed in the power system, with the use of CM.
In zero sequence, which is not shown in figure 2.1 for clarity, both CPP and WPP give
the same response since they both employ dYN transformers, which are grounding the
neutral of the grid side, and also isolating the zero sequence networks of power plant
and the grid side. Hence zero sequence currents flow, and zero sequence voltage is
attenuated towards the power plants in both cases.
24
Chapter 2 Identified Problems during Grid Faults
Figure 2.1 SLG response of (a) CPP, (b) WPP with zero current, (c) WPP with CM.
Detailed analysis of the identified problems, and control solutions during asymmetrical
faults will be given in chapter 6 and 7, respectively. In the following part of this chapter
and consequent chapters (3, 4, and 5), analysis of problems and solutions for the
symmetrical faults will take place.
25
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
2.2 Loss of Synchronism during Symmetrical Grid Faults
2.2.1
Simulation Case
Structure of a generic WPP, utilized in this chapter, is shown in figure 2.2. The WPP
has a rating of 100MW and composed of 20 of FSCWTs each having 5MW ratings.
The WPP is aggregated as a single wind turbine with equivalent of collector grid. The
wind turbine is performing grid synchronization and current control action at the low
voltage side of the WT transformer. The impedance between the WT control terminal
and the PCC has a magnitude of 0.21pu with and X/R of 8, which is composed of the
WT transformer, collector grid, and the WPP main transformer. The PCC is connected
to the main grid via a 20km line, which has impedance of 0.1pu with X/R of 4. The
main grid is represented with its Thevenin equivalent with impedance of 0.1pu and X/R
of 10 (SCR is 10).
Fig. 2.2 Aggregated WPP diagram and Thevenin equivalent grid of simulation study.
Within the simulation cases in this section, a symmetrical short-circuit fault is created
at the PCC point, where the fault impedance is adjusted to have remaining voltage
magnitudes as 2%, also 10% and 25% of the rated during the faults. The fault is created
at time is equal to 1 second and removed at time is equal to 1.4 second, as will be seen
in the following simulation results.
The grid synchronization algorithm, PLL, implemented within the WT is shown in
figure 2.3 below. As well-known, within the PLL, a frequency signal is calculated,
which is integrated to obtain the phase angle of WT terminal voltage, șwt. The
estimated angle șwt is used within the current control algorithms to obtain active and
reactive current components and to generate necessary voltage at the converter output.
26
Chapter 2 Identified Problems during Grid Faults
For observation of a clean frequency signal without transients a Low-Pass Filter, which
has a cut-off frequency of 30Hz, is applied to the raw frequency signal in simulation
results.
vq
vd
Fig. 2.3 Generic PLL structure.
Three fault cases, cases 1 to 3, where the PCC voltage drops to 2% of the rated, are
shown in the following sections.
In case-1 (figure 2.4), the WT is injecting pure reactive current with magnitude of 1pu
during the low voltage fault. In this case, the WT frequency, which is the frequency of
the voltage at the WT terminals calculated by the PLL, drops down close to 0Hz during
the fault. In other words, frequency of the voltage and current generated by the WT
drop down to 0Hz; though the frequency at the faulted point (PCC) is still around
50Hz. This event is called as Loss of Synchronism (LOS) - frequency fall, which will
be studied in the following chapters.
In case-2 (figure 2.5), the WT is injecting 1pu reactive current and 0.125pu active
current during the low voltage fault. However, for certain reasons, which will be given
in the next chapters, the WT frequency stays stable (synchronized to the grid) around
50Hz in this case.
In case-3 (figure 2.6), the WT injects highly active current of 0.65pu magnitude and
still 1pu reactive current, which results in total current magnitude of 1.2pu, i.e. WT
injects more than the rated 1pu value during fault. In this case of highly active current
injection the frequency of the voltage at the WT terminal increases towards very high
values, such as 100 Hz, due to the reasons that will be explained in the following
chapters. This event is called as LOS – frequency rise.
In section 2.2.5, results of these simulation cases and six more cases with higher PCC
voltages during the faults, is summarized in a single figure, showing whether stable
27
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
operation around 50Hz or LOS is observed. It is important to mention that in case of
zero current injection during the fault, which is not shown here, WT stays synchronized
to 50Hz. Hence the LOS is observed only if current injection during fault is
accomplished by wind turbines.
2.2.2
Fault Case-1: Loss of Synchronism – Frequency Fall
As observed in the last subfigure of figure 2.4, for a severe fault and pure reactive
current injection case, frequency calculated and used within the PLL of wind turbine
decreases towards zero, therefore voltage and current generated by the WT have low
frequency as observed in third and fourth subfigures.
Vpcc-abc&rms
(pu)
Case-1
Iwt Active&Reactive
(pu)
Vpcc =2%
Ireactive=1pu
Iactive=0pu
șI=90°
1
Vpcc-a
Vpcc-b
Vpcc-c
|Vpcc|-50Hz
0
-1
0.9
Vwt-abc&rms
(pu)
Fault at PCC
1
1.1
1.2
1.3
1.4
1.5
1.6
2
Ireact - ref
Ireact - meas
Iact - ref
Iact - meas
1
0
-1
-2
0.9
1
1.1
1.2
1.3
1.4
1.5
1
Vwt-a
Vwt-b
Vwt-c
|Vwt|-50Hz
0
-1
0.9
1.6
1
1.1
1.2
1.3
1.4
1.5
1.6
Iwt-abc&rms
(pu)
2
0
-1
-2
0.9
WT frequency
(Hz)
Iwt-a
Iwt-b
Iwt-c
|Iwt|-50Hz
1
50
40
30
20
10
0
0.9
1
1.1
1.2
1.3
1
1.1
1.2
1.3
Fig. 2.4 Case-1: Loss of Synchronism – Frequency Fall.
28
1.5
1.6
WT frequency
time (s)
1.4
1.4
1.5
1.6
Chapter 2 Identified Problems during Grid Faults
2.2.3
Fault Case-2: Synchronized to 50Hz
As observed in the last subfigure of figure 2.5, for a severe fault and injection of a
current with specific active and reactive components, LOS is not experiences and the
frequency calculated and used within the PLL of the wind turbine remains around 50
Hz, where the reasons are explained in the following chapters.
Vpcc-abc&rms
(pu)
Case-2
Iwt Active&Reactive
(pu)
Ireactive=1pu
Iactive=0.125pu
șI=83°
1
Vpcc-a
Vpcc-b
Vpcc-c
|Vpcc|-50Hz
0
-1
0.9
Vwt-abc&rms
(pu)
Vpcc =2%
Fault at PCC
1
1.1
1.2
1.3
1.4
1.5
1.6
2
Ireact - ref
Ireact - meas
Iact - ref
Iact - meas
1
0
-1
-2
0.9
1
1.1
1.2
1.3
1.4
1.5
1
Vwt-a
Vwt-b
Vwt-c
|Vwt|-50Hz
0
-1
0.9
1.6
1
1.1
1.2
1.3
1.4
1.5
1.6
Iwt-abc&rms
(pu)
2
0
-1
-2
0.9
WT frequency
(Hz)
Iwt-a
Iwt-b
Iwt-c
|Iwt|-50Hz
1
50
40
30
20
10
0
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
WT frequency
1
1.1
1.2
1.3
1.4
1.5
1.6
time (s)
Fig. 2.5 Case-2: Stable operation – synchronized to 50Hz.
29
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
2.2.4
Fault Case-3: Loss of Synchronism – Frequency Rise
As observed in the last subfigure of figure 2.6, for a severe fault and injection of high
active current component together with 1pu reactive component case, the frequency
calculated and used within the PLL of the wind turbine increases towards high values
(e.g. 100Hz), therefore voltage and current generated by the WT have high frequency
as observed in third and fourth subfigures.
Vpcc-abc&rms
(pu)
Case-3
Fault at PCC
Vpcc =2%
Ireactive=1pu
Iactive=0.65pu
șI=57°
1
Vpcc-a
Vpcc-b
Vpcc-c
|Vpcc|-50Hz
0
-1
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
Iwt Active&Reactive
(pu)
2
Ireact - ref
Ireact - meas
Iact - ref
Iact - meas
1
0
-1
-2
0.9
1
1.1
1.2
1.3
1.4
1.5
Vwt-abc&rms
(pu)
1
Vwt-a
Vwt-b
Vwt-c
|Vwt|-50Hz
0
-1
0.9
1.6
1
1.1
1.2
1.3
1.4
1.5
1.6
Iwt-abc&rms
(pu)
2
Iwt-a
Iwt-b
Iwt-c
|Iwt|-50Hz
1
0
-1
y
150
q
(Hz)
-2
0.9
100
1
1.1
1.2
1.3
1.4
1.5
1.6
WT frequency
50
0
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
time (s)
Fig. 2.6 Case-3: Loss of Synchronism – Frequency Rise.
2.2.5
Fault Cases with 0.1pu and 0.25pu PCC Voltages
In addition to three cases (1 to 3) of previous sections with results given in figures 2.4
to 2.6, where the PCC voltage was dropping to 2% of the rated value, six more cases (4
to 9) are simulated. In cases 4 to 6, PCC voltage drops to 10%; and in cases 7 to 9, PCC
30
Chapter 2 Identified Problems during Grid Faults
voltage drops to 25% of the rated value. The simulation results for cases 4 to 9 are not
shown to save space and since similar time-domain results (LOS as frequency fall/rise
or stable operation at 50Hz) are observed. The overall results of total nine cases are
given in figure 2.7. As seen in figure 2.7 case-6, LOS is observed also when the PCC
voltage is 10% of rated and high active current is injected accompanying the 1pu
reactive current.
I wt =I șI =1pu 90o
I wt =I șI =1.01pu 83o
ș I =90
o
ș I =83
o
ș I =90
o
ș I =83
o
ș I =90
o
ș I =83
o
I wt =I șI =1.2pu 57o
ș I =57
o
ș I =57
o
ș I =57
o
Fig. 2.7 Results with respect to active and reactive current components and PCC
voltage.
31
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
As given in the previous figures, during the LOS events, frequency of the WT deviates
from the fundamental 50Hz frequency of the grid. It is interesting but proven to be true
(with simulation and experiment results in following chapters) that the frequency of the
voltage at the WT terminal becomes 0Hz (DC) or larger than 100 Hz while the faulted
grid point (in this case PCC) voltage is still at 50 Hz. Phase voltages from previous
results are given in figures 2.8 and 2.9 to clearly show the mentioned events.
It is seen in figure 2.8 that during the LOS – frequency fall event, the WT voltage drops
almost to 0Hz (DC signal) while the PCC voltage is still around 50Hz. Similarly in
figure 2.9, during the LOS – frequency rise event, the WT voltage is above 100Hz,
while the PCC voltage is still at 50Hz. Inevitably, the current injection from the WT,
which has 0 or 100 Hz frequency, cause some amount of distortion at the PCC voltage
as observed in figures 2.8 and 2.9.
0.1
Vpcc-a
Vpcc-b
Vpcc-c
|Vpcc|-50Hz
0.08
0.06
Vpcc-abc&rms
(pu)
0.04
0.02
0
-0.02
-0.04
-0.06
-0.08
-0.1
0.2
Vwt-a
Vwt-b
Vwt-c
|Vwt|-50Hz
0.15
Vwt-abc&rms
(pu)
0.1
0.05
0
-0.05
-0.1
-0.15
-0.2
1.3
1.32
1.34
1.36
1.38
time (s)
Fig. 2.8 Trace of PCC and WT voltages in figure 2.4 (between 1.3 and 1.4 seconds)
32
1.4
Chapter 2 Identified Problems during Grid Faults
0.1
Vpcc-a
Vpcc-b
Vpcc-c
|Vpcc|-50Hz
0.08
0.06
Vpcc-abc&rms
(pu)
0.04
0.02
0
-0.02
-0.04
-0.06
-0.08
-0.1
1
Vwt-a
Vwt-b
Vwt-c
|Vwt|-50Hz
0.8
0.6
Vwt-abc&rms
(pu)
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
-1
1.3
1.32
1.34
1.36
1.38
1.4
time (s)
Fig. 2.9 Trace of PCC and WT voltages in figure 2.6 (between 1.3 and 1.4 seconds)
As a summary of the results in figure 2.7, it can be commented that LOS occurs in
some specific cases depending on the remaining voltage at the faulted bus (PCC) and
the active-reactive current magnitudes. Being not shown here, it has been observed that
the occurrence of the LOS event also depends on the characteristics (magnitude and
angle) of the impedance between the WT and the faulted point (e.g. PCC). It is
important to state that in case of zero current injection during the fault, which is not
shown here; WT stays synchronized to 50Hz. Also, for the faults occurring on the line
between the PCC and main grid, or at the bus where the line is connected to the main
grid, similar LOS events have been observed.
In practical wind turbines in a real WPP, or the protection units within WPP would trip
if such a frequency deviation is measured during a fault. Additionally, as observed in
figures 2.4 and 2.6, if a LOS event occurs during the fault, WT is not able to restore its
normal 50Hz operation even after the fault is cleared and PCC voltage recovers.
33
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
2.2.6
PLL with Saturation and Anti-Windup Algorithm
The PLL structure shown in figure 2.3 does not include any saturation block within its
PI controller or at the calculated frequency signal output. In practical saturation blocks
are employed for the integrator blocks and a limit is applied to the calculated
frequency. When the output of the integrator is limited to the saturation value, the state
of the integrator also needs to be limited to the saturation value, i.e. an anti-windup
algorithm is needed, to avoid windup of integrator. The described saturation blocks are
included in the PLL structure in Figure 2.10 below. As an example, the frequency
signal can be limited to be maximum 55Hz and minimum 45Hz.
vq
vd
Fig. 2.10 PLL structure with saturation and anti-windup algorithms.
The impact of PLL saturation blocks on the LOS problem will be handled again in
chapter 4 and 5. It should be stated here that the LOS –frequency fall/rise events are
observed for cases 1, 3, and 6 (of figure 2.7), also when the PLL structure with
saturation functions in Figure 2.10 is employed. However, when the saturation blocks
are employed, the frequency falls or rises until the limit values, e.g. 45 Hz or 55Hz,
while the PCC voltage is still around 50Hz.
2.2.7
Physical Understanding of LOS
In order to better explain LOS event physically, figure 2.11 is given below. As seen in
the figure, when a severe (solid) fault close to PCC or at the PCC occurs, WPP
experiences a very low grid voltage and as explained above, LOS occurs during current
injection from wind turbines to the low voltage. The WPP side of the network behaves
like “isolated” from the main grid side, which continues with 50Hz unless it is an
unstable system. As shown in figure 2.11-(b), in such a fault case the wind turbine is
injecting current to the low voltage at the faulted point through impedance Z (R+jX),
34
Chapter 2 Identified Problems during Grid Faults
which is composed of the impedance of the WT transformer, WPP collector grid, WPP
transformer, and the connection line. During severe grid faults the faulted point voltage
drops down close to zero and wind turbines are injecting controlled active and reactive
currents to a resistive inductive (R-X) impedance load with a very low voltage behind.
As will be shown in the next chapters, if active and reactive current references are not
convenient with the impedance characteristics, LOS occurs as shown in this chapter. In
the following chapters analysis of the LOS and novel control methods will be proposed
to provide stable operation of the WPP side of the network avoiding LOS.
Fig. 2.11. Representative (a) two “isolated” networks during current injection to severe
faults, (b) with Thevenin equivalent of main grid.
35
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
2.3 Conclusion
According to recent grid codes, wind turbines are required to inject reactive currents
during faults proportional to the voltage drop at their connection terminals, even for
severe faults, where the voltage drops down to zero, and also for asymmetrical faults.
In this chapter, details of the identified problems, which occur with the use of the
conventional current reference generation methods during asymmetrical and severe
symmetrical faults, are given.
In order to show the dependency of the LOS event to the active and reactive current
injection and PCC voltage, nine different cases have been simulated. Throughout the
following chapters, simulations results will be analyzed with theory and verified with
experimental results. In the next chapter, active and reactive current transfer limits will
be derived. In chapter 4, where the LOS event will be analyzed, the results of these
nine cases will be correlated with the active and reactive current transfer limits.
36
Chapter 2 Identified Problems during Grid Faults
37
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
Chapter 3
Active and Reactive Current Transfer Limits
In this chapter, a basic but fundamental theory; active and reactive current transfer
limits between two buses are explored as a function of voltage magnitude at the
receiving bus, and the line impedance between the buses. It is shown that when active
and reactive current control (vector control) is performed to inject current through
impedance, certain current transfer limits exist, which have not been considered
before. The derived limits play an important role to understand the Loss of
Synchronism (LOS) phenomenon occurring during active and reactive current injection
from wind turbines to severe symmetrical grid faults. The impact of taking the
resistance of the line into account especially for low voltage situations is emphasized.
The correlation of derived active and reactive current transfer limits to a WPP case
and to the grid code requirements are given at the end.
3.1 Active and Reactive Power Flow between Two Buses
For a better understanding of current limits, active and reactive power transfer limits
between two buses, which is a well-known classical power system theory, is given first.
3.1.1
Power Flow on a Line neglecting the Resistance
Two buses, which are connected through a line, with voltages V1 and V2 and their
phasor diagram are shown in figure 3.1 below. Since transmission lines in a power
system are highly inductive with low resistance, as a general approach, resistive
component of the line is neglected when power-angle characteristics are derived.
38
Chapter 3 Active and Reactive Current Transfer Limits
V1 TV
V1 TV
V2 0D
I
Z
jX
Z. I
TV
I
V2 0
D
Fig. 3.1 Power flow on a lossless line; single-line diagram and phasor diagram.
Neglecting the resistive component of the line, active and reactive power-angle
characteristics at the sending end (V1) of the diagram above is defined as (3.1) and (3.2)
below, which are well-known from classical power system theory.
P1 =
V1V2
sinș V
X
(3.1)
V12 -V1 V2 cosș V
X
(3.2)
Q1 =
In figure 3.2, power-angle characteristics are drawn for a healthy situation with V1 and
V2 having rated magnitudes of 1pu with a line of Z=j0.4pu. In figure 3.3, voltage V2
drops down to 0.05pu and V1 drops down to 0.3pu, still being higher than V2. In figure
3.4, voltage V2 drops to zero while V1 is 0.3pu.
As seen from (3.1), (3.2) and figure 3.3, and well-known from power system theory,
active power limit flow from sending end substantially decreases for low voltage
situations. As seen from figure 3.4, when the sending end (V1) voltage is 0.3pu and the
receiving end (V2) voltage is zero, active power flow becomes zero and a certain
amount of reactive power flows. Active and reactive power equations for zero V2 are
given below;
V2
0
Ÿ
P1 =0
and
Q1 =
V12
X
(3.3)
Remark 3.1:
Observing figure 3.4 and (3.3), where reactive power is flowing from sending end,
without supplying any active power flow, a comment like “pure reactive power can be
supplied to a zero voltage bus through a line without supplying any active power” can
be done, which is incorrect since the resistive component of the line has been neglected
39
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
in the calculations. However, practically lines do have non-zero resistive component, of
value depending on the line characteristics and temperature. In the next section, powerangle characteristics are derived considering the resistive component of the line.
2
1
0
-1
-2
-360
-270
-180
-90
0
90
180
270
360
-270
-180
-90
0
90
180
270
360
5
4
3
2
1
0
-1
-360
ɽV (degrees)
Fig. 3.2 Power -angle characteristics for V1=V2=1pu and Z=j0.4pu
0.5
0
-0.5
-360
-270
-180
-90
0
90
180
270
360
-270
-180
-90
0
90
180
270
360
0.5
0
-0.5
-360
ɽV (degrees)
Fig. 3.3 Power -angle characteristics for V1 =0.3pu, V2=0.05pu, and Z=j0.4pu
40
Chapter 3 Active and Reactive Current Transfer Limits
0.5
0
-0.5
-360
-270
-180
-90
0
90
180
270
360
-270
-180
-90
0
90
180
270
360
0.5
0
-0.5
-360
ɽV (degrees)
Fig. 3.4 Power -angle characteristics for V1=0.3pu, V2=0pu, and Z=j0.4pu
3.1.2
Power Flow on a Line considering the Resistance
In this section power flow characteristics between two buses is derived while taking the
resistive component of the line into account. Two buses, which are connected through a
line, with voltages V1 and V2 and their phasor diagram are shown in figure 3.5 below.
V1 T V
V1 TV
V2 0D
I
Z
R jX
Z. I
TV
I
V2 0
D
Fig. 3.5 Power flow on an inductive/resistive line; single-line diagram and phasor
diagram.
Active and reactive power equations with consideration of the line resistance are given
below, where Z represents magnitude of the impedance;
41
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
Rcosș
V1V2 X
V12R VV
P1 = 2 sinșV + 2 1 2 2 V
Z
Z
Z
Q1 =
(3.4)
V12 X V1 V2 Xcosș V V1 V2 Rsinș V
Z2
Z2
Z2
(3.5)
In the following three figures, power-angle characteristics are drawn for different bus
voltage magnitudes for a line having an impedance as 0.08pu+j0.4pu, i.e. with an X/R
ratio of 5. In figure 3.6, power-angle characteristics are drawn for a healthy situation
with V1 and V2 having identical magnitudes of 1pu. In figure 3.7, voltage V2 drops
down to 0.05pu and V1 drops down to 0.3pu, still being higher than V2. In figure 3.8,
voltage V2 drops to zero while V1 is 0.3pu.
As seen from (3.4) and figure 3.7, and well-known from power system theory, active
power flow substantially decreases for low voltage situations. However, in this case,
where line resistance is taken into account, active power takes values larger than zero
for any angle (șV) value. Similarly, in figure 3.8, where the sending end (V1) voltage is
0.3pu and receiving end (V2) voltage is zero, certain amount of reactive power, but also
a non-zero amount of active power flow are observed. Active and reactive power
equations for zero V2 are given below;
V2 0
Ÿ
P1 =
V12R
V12X
and
Q
=
1
Z2
Z2
Ÿ
P1 R
=
Q1 X
(3.6)
It is obvious that when the receiving end voltage, V2, is zero, the active and reactive
power flowing from sending end to the receiving end is dissipated as active (I2R) and
reactive (I2X) power losses on the resistance and reactance of the line.
42
Chapter 3 Active and Reactive Current Transfer Limits
3
2
1
0
-1
-2
-360
-270
-180
-90
0
90
180
270
360
-270
-180
-90
0
90
180
270
360
5
4
3
2
1
0
-1
-360
ɽV (degrees)
Fig. 3.6 Power -angle characteristics for V1=V2=1pu and Z=0.08+j0.4pu
0.5
0
-0.5
-360
-270
-180
-90
0
90
180
270
360
-270
-180
-90
0
90
180
270
360
0.5
0
-0.5
-360
ɽV (degrees)
Fig. 3.7 Power -angle characteristics for V1=0.3pu, V2=0.05pu, and Z=0.08+j0.4pu
43
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
0.5
0
-0.5
-360
-270
-180
-90
0
90
180
270
360
-270
-180
-90
0
90
180
270
360
0.5
0
-0.5
-360
ɽV (degrees)
Fig. 3.8 Power -angle characteristics for V1=0.3pu, V2=0pu, and Z=0.08+j0.4pu
Following remarks can be done based on the observations above;
Remark 3.2:
Observing figures 3.7 and 3.8 it can be stated that in case of very low (or zero)
receiving end voltage; for reactive power flow from sending end (i.e. V1 >V2), active
power injection cannot be zero. Referring to the remark 3.1 in previous section, it is
important to note that, pure reactive power flow from sending end requires a voltage,
which is not very low (neither zero), at the receiving end.
In order to provide reactive power flow from sending end (i.e. V1>V2) a certain amount
of non-zero active power supply from the sending end is required. An explanation for
this situation can be that; the amount of active power loss (arising with the reactive
power flow) on the resistive component of the line has to be compensated by the
sending end, since this amount cannot be supplied by the receiving end, which has very
low (or zero) voltage.
Remark 3.3:
Similar to the remark 3.2, for active power flow from sending end, reactive power
injection cannot be zero. The reason for this situation is that the reactive power loss
44
Chapter 3 Active and Reactive Current Transfer Limits
(arising with the active power flow) on the inductive component of the line has to be
compensated by the sending end, since it cannot be supplied by the receiving end,
which has very low (or zero) voltage.
Remark 3.4:
Observing figure 3.7, where V2 is very low, and especially figure 3.8 and (3.6), where
V2 is zero, it can be stated that for a fixed amount of reactive power injection, active
power injection cannot be lower or higher than a fixed amount. Similarly, for a fixed
amount of active power injection, reactive power injection cannot be lower or higher
than a fixed amount. As seen in (3.6), proportionality between active and reactive
power injection when V2 is zero, depends on the line X/R characteristics, i.e. the line
characteristics dictates the dependency between active and reactive power.
These remarks play important role in order to help understanding of the active/reactive
current transfer limits in the following parts.
3.2 Active and Reactive Current Flow between Two Buses
Since the focus of this thesis is on the current injection by wind turbines, current
transfer characteristics from one bus to another bus through impedance are analyzed in
this part. First, the current-angle characteristics are given, and then the active/reactive
current transfer limits as a function of the receiving bus voltage magnitude and line
impedance (R+jX) are derived.
3.2.1
Current - Angle Characteristics
The current is defined as the active and reactive currents injected from the sending end
(V1) as shown in figure 3.9 below. Current-angle characteristics can be easily obtained
as (3.7) and (3.8) below using power-angle characteristics (3.4) and (3.5) from previous
section;
Iactive =
P1 V2X
V R V Rcosș
= 2 sinșV + 1 2 - 2 2 V
V1 Z
Z
Z
Ireactive =
Q1 V1 X V2XcosșV V2RsinșV
= 2 V1
Z
Z2
Z2
(3.7)
(3.8)
45
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
V1 T V
V1 TV
V2 0D
Id (Iactive )
Z=R+jX=Z ɽZ
Z. I
TV
I
V2 0
D
Iq (I reactive )
Fig. 3.9 Current flow on an inductive/resistive line; single-line diagram and phasor
diagram
As observed in figure 3.10, for a line with impedance Z=0.08+j0.4, when sending end
voltage V1 drops to 0.3pu and the receiving end voltage V2 to 0.05pu, the active current
gets non-zero values for any angle, șV. In figure 3.11, when V2 drops down to zero, a
fixed amount of active and reactive current flows, similar to the previous power flow in
figures 3.7 and 3.8.
ɽV (degrees)
Fig. 3.10 Current -angle characteristics for V1=0.3pu, V2=0.05pu, and Z=0.08+j0.4pu
46
Chapter 3 Active and Reactive Current Transfer Limits
0.5
0
-0.5
-360
-270
-180
-90
0
90
180
270
360
-270
-180
-90
0
90
180
270
360
0.5
0
-0.5
-360
ɽV (degrees)
Fig. 3.11 Current -angle characteristics for V1=0.3pu, V2=0pu, and Z=0.08+j0.4pu
Based on (3.7) and (3.8), for V2=0 and V1>0, active and reactive currents can be
obtained as (3.9) below;
V2 0
Ÿ
Iactive =
V1 R
VX
and Ireactive = 1 2
2
Z
Z
Ÿ
Iactive R
=
Ireactive X
(3.9)
It is obvious that when the receiving end voltage, V2, is zero, the active and reactive
currents flowing from sending end to the receiving end creates only active (I2R) and
reactive (I2X) losses on the resistance and reactance of the line.
Remark 3.5:
Observing figure 3.10, where V2 is very low, and especially figure 3.11 and (3.9),
where V2 is zero, it can be stated that for a fixed amount of reactive current injection,
active current injection cannot be lower or higher than a fixed amount. Similarly, for a
fixed amount of active current injection, reactive current injection cannot be lower or
higher than a fixed amount. As seen in (3.9), proportionality between injected active
and reactive currents when V2 is zero, depends on the line X/R characteristics, i.e. the
line dictates the dependency between active and reactive currents.
47
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
3.2.2
Derivation of Active and Reactive Current Transfer Limits
In previous sections power-angle and current-angle characteristics are analyzed,
however power and current equations were based on given V1 and V2, and varying șV.
However, wind turbines are injecting controlled active and reactive currents (as vector
control) at their terminals. For instance, when the receiving end voltage V2 (e.g. PCC
voltage) drops to a low voltage value, active and reactive currents are injected from the
sending end V1 (WT terminal). Hence, it is more than necessary to analyze the active
and reactive current injection operating points as a function of (low) voltage magnitude
at the receiving end (V2) and the line impedance (R+jX). In order to derive the active
and reactive current operating points, single-line diagram in figure 3.12 and phasor
diagram in figure 3.13-(a) are utilized. Since active and reactive currents are injected
with reference to V1, the V1 voltage is located on the horizontal axis, and controlled
current phasor with respect to V1 is shown with current angle șI. With the positive
value of șI and Iq (reactive current) the wind turbine is injecting reactive power
(overexcited operation, equivalent to capacitive behavior).
In order to find the magnitude limit for a current injection with angle șI, the diagram in
figure 3.13-(b) is used, similar to the one given in [56]. Regarding the constraint that
magnitude of V2 is fixed, a circle with radius equal to the magnitude of V2 voltage is
drawn. Then, V2 voltage is found via locating the voltage phasor on the impedance (ZI)
such that the tip of the ZI is on the circle and the end of the ZI is on the V1 reference
axis, while keeping the angle of ZI with respect to V1 fixed at șI–șZ. As expected,
magnitude of V1 is varied while locating ZI. In the following parts, for every current
angle, i.e. șI from 0° to 360°, the limit value for the current magnitude is found, while
keeping constant V2 value and Z (R+jX). It is important to note that the impedance
includes a resistive component, i.e. șZ<90°, in the following phasor diagrams.
V1 TV
V2 0D
Z
R jX
Fig. 3.12 Single line diagram used for derivation of current limits.
48
Chapter 3 Active and Reactive Current Transfer Limits
V2 constant
Id (Iactive )
TI
Iq (I reactive )
V2
V1
-Z.I
T I -T Z V1
TI
constant
I
I
Fig. 3.13 Current phasor (a) and methodology (b) to derive limits.
Current magnitude limit for șI=90° (pure reactive):
As the first step, using methodology described above, current magnitude limit is
derived for pure reactive current injection, i.e. șI=90°, below.
V2 constant
V2
ș I =90
I
V2
-Z.Ilimit
-Z.I
o
T I -T Z V1
ș I =90
constant
o
T I -T Z V1
constant
I=Ilimit
Fig. 3.14 Current transfer limit for șI=90° (pure reactive).
As seen in figure 3.14-(a), with a low current magnitude an operating point can be
found. However, when the current magnitude reaches a level, called as Ilimit, as shown
in figure 3.14-(b), the angle difference between V1 and V2 becomes 90°. This is the
point where the largest phasor ZI can be located with the constraint of constant V2
magnitude and fixed at șI – șZ . Figure 3.15 is given to better explain this statement. If
the current magnitude becomes larger, magnitude of the phasor ZI becomes larger as
expected. However, with this large magnitude of ZI phasor and fixed angle with respect
to V1, șI–șZ, the ZI phasor can only be located between V1 reference line and reference
line-2, shown in figure 3.15. Therefore, the tip of the ZI phasor cannot intersect with
the V2 circle, which implies that a larger V2 is required, which means that there is not
49
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
any operating point with I> Ilimit and șI=90°. In other words, for the current injection
angle, șI=90°, the current transfer limit is found as in figure 3.14-(b) and (3.10).
reference line 2
V2 constant
-Z.I
ș I =90
o
V1 reference line
V1 T I -T Z
constant
I>Ilimit
Fig. 3.15 Out of transfer limit situation for I> Ilimit and șI=90°.
The current transfer limit for șI=90° can be calculated from figure 3.14-(b), as below;
șI =90o
Ÿ V2 =Z.Ilimit .sin(șI -șZ ) Ÿ Ilimit =
V2
Z.cos(șZ )
Ÿ Ilimit =
V2
(3.10)
R
Remark 3.6:
Observing figure 3.15, when the pure reactive current magnitude is larger than the limit
value given in (3.10), an operating point cannot be found, due to small magnitude of
V2. This means that for a very low receiving end voltage, it is not possible to inject
unlimited pure reactive current with zero active current, which was also commented for
pure reactive power in remark 3.2 and 3.5 in previous sections.
It is also important to note that this situation arises due to resistive (R) component of
the line. If R was zero, an operating point would always be found, i.e. limit would be
infinity in (3.10). However, since it is not practically possible to have R as zero, it is
not possible to have operating point with pure reactive current larger than the limit in
(3.10).
Observing (3.10), it can be commented that, when the receiving end voltage drops to
very low values and/or resistive component becomes larger, limit value becomes
smaller.
50
Chapter 3 Active and Reactive Current Transfer Limits
The limit value obtained in this section is imposed on the active/reactive current axes in
figure 3.16 below. This plot is filled throughout this section for all current angles.
șZ
V2
R
ș I =90o
Fig. 3.16 Active/reactive current transfer limits
Current magnitude limit for 90° > șI > șZ:
From figure 3.17-(a) to 3.17-(b), magnitude of current is increased while keeping the
angle constant at șI until the phase difference between V1 and V2 reaches 90°, which is
largest current magnitude with a possible operating point. As explained in the previous
part, any current larger than this magnitude would require a higher V2 magnitude.
V2 constant
V2 -Z.I
T I T I -T Z V1
V2
-Z.Ilimit
TI
I
T I -T Z
V1
I=Ilimit
Fig. 3.17 Current magnitude limit for 90° > șI > șZ.
Following the same methodology as previous case, the current transfer limit as a
function of V2, Z and șI , for 90°>șI>șZ is found from figure 3.17-(b) as;
90o ! șI > șZ
Ÿ V2 =Z.Ilimit .sin(șI -șZ ) Ÿ Ilimit =
V2
Z.sin(șI -șZ )
(3.11)
51
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
The derived limit is added to the active/reactive current axes as in figure 3.18. The
possible operating points are shown as the green-shaded area. It is important to note
that the formula of Ilimit in (3.11) results in a straight line while șI is varying between
90° and șZ.
șZ
V2
R
șI
I limit =
V2
Zsin(ș I -ș Z )
Fig. 3.18 Active/reactive current transfer limits-2.
Remark 3.7:
It is important to note that for a fixed current injection angle as in figures 3.14 and 3.17,
the angle difference between the sending end (V1) and receiving end (V2) voltage
increases, which reaches 90° at the limit point. Also for a fixed current magnitude, this
angle difference between two bus voltages increase in proportion with the deviation of
the current angle from the impedance angle, șZ. This remark will be important for the
small-signal stability analysis in the next chapter.
Remark 3.8:
Observing the current phasor and the receiving end voltage V2 phasor in figures 3.14(a) and 3.17-(b), it is seen that current phasor has a component anti-phase with V2;
which implies that active power is absorbed from the V2 bus. This means that, for
highly (or pure) reactive current injection, the current phasor at the receiving end bus
takes a form of highly active, but as consumption. Observing figure 3.14-(b), when the
limit is reached for pure reactive current, there is only active current (consumption) at
the receiving end bus. This means that the reactive power supplied by the V1 bus is
52
Chapter 3 Active and Reactive Current Transfer Limits
consumed as I2X loss on the line, and the I2R loss (arising with the reactive current
flow) is absorbed from the V2 bus.
Current magnitude limit for șI = șZ:
In figure 3.19, magnitude of current is increased while keeping the angle constant equal
to the impedance angle, șI=șZ. Different from the previous injection angles, when the
current is injected with the angle of the impedance (șZ), a limit such as in figures 3.14(b) or 3.17-(b) is not reached. There is always an operating point, and there is not a
limit for the current transfer with this angle.
V2 constant
V2
ș I =ș Z
-Z.I
V1
V2
ș I =ș Z
-Z.I
V1
I
I
Fig. 3.19 Current magnitude limit for șI = șZ.
It should be noted that, as observed in figure 3.19, V1 magnitude is increasing with
increasing current magnitude. Hence, at some point V1 would reach high values, which
means that there would be a limit due to voltage limitations at the sending end V1.
However, in case of fault conditions, due to low voltage at V2 and limited current
ratings, V1 would not increase above rated value; hence mentioned current limit due to
voltage limit is not shown here for clarity.
The current injection, which is not limited when current has the angle of the
impedance, is imposed to the active/reactive current operating point plot as in figure
3.20.
53
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
șZ
V2
R
ș I =ș Z
I limit =
V2
Zsin(ș I -ș Z )
Fig. 3.20 Active/reactive current transfer limits-3.
Current magnitude limit for șZ > șI > 0°:
In figure 3.21, magnitude of current is increased while keeping the angle constant at șI
until the phase difference between V1 and V2 reaches 90°, which is largest current
magnitude with a possible operating point. As explained in the previous part, any
current larger than this magnitude would require a higher V2 magnitude. Different from
the previous cases, where highly reactive (overexcited/capacitive) current was being
injected and V1 was increasing with increasing current magnitude, here V1 magnitude is
decreasing with increasing current since highly active current is injected
V2 constant
T Z -T I
TI
V1
-Z.I
I V2
(a)
T Z -T I V
1
TI
-Z.Ilimit
V2
I=Ilimit
(b)
Fig. 3.21 Current magnitude limit for șZ > șI > 0°.
Following the same methodology as previous case, the current magnitude limit for
șZ>șI>0° is found from figure 3.21-(b) as;
54
Chapter 3 Active and Reactive Current Transfer Limits
șZ ! șI > 0o
Ÿ
V2 =Z˜ Ilimit ˜ sin(șZ -șI ) Ÿ
Ilimit =
V2
Z.sin(șZ -șI )
(3.12)
The derived limit is imposed to the active/reactive current operating point plot as in
figure 3.22. The possible operating points are shown as the green-shaded area.
șZ
V2
R
șI
I limit =
I limit =
V2
Zsin(ș Z -ș I )
V2
Zsin(ș I -ș Z )
Fig. 3.22 Active/reactive current transfer limits-4.
Current magnitude limit for șI = 0° (pure active):
In figure 3.23, magnitude of current is increased while keeping the angle constant at șI=
0° (pure active) until the phase difference between V1 and V2 reaches 90°, which is the
largest current magnitude with a possible operating point. It should be noted that V1
drops down towards zero since pure active current is being injected.
V2 constant
I V1 T Z -T I
T Z -T I V1
V2 -Z.I
I=Ilimit
-Z.Ilimit
V2
Fig. 3.23 Current magnitude limit for șI = 0° (pure active).
Following the same methodology as previous case, the current magnitude limit for
șI=0° is found from figure 3.23-(b) as;
55
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
șI =0o
Ÿ
V2 =Z.Ilimit .sin(șZ -șI ) Ÿ
Ilimit =
V2
Z.sin(șZ )
Ÿ
Ilimit =
V2
X
(3.13)
Remark 3.9:
Observing figure 3.23, it is seen that an operating point cannot be found, when the pure
active current magnitude is larger than the limit value given in (3.13). This means that
for a very low receiving end voltage, it is not possible to inject unlimited pure active
current with zero reactive current, which was also commented for active power transfer
in remark 3.3 and 3.5 in previous sections.
Observing (3.13), it can be commented that, when the receiving end voltage drops to
very low values and/or inductive component becomes larger, pure active current limit
value becomes smaller, which is a well-known concern for active power injection to a
weak grid. The derived limit is imposed to the active/reactive current operating point
plot as in figure 3.24. The possible operating points are shown as the green-shaded
area.
As seen in figure 3.23, with increasing active current magnitude, the angle difference
between V1 and V2 reaches 90°, which is known as the maximum transferrable active
power point in power system theory. However, as increasing reactive power injection
increases the active power transfer limit, increasing reactive current can increase the
active current transfer limit, as shown in figure 3.24 below.
Remark 3.10:
Observing the current phasor and the receiving end voltage V2 phasor in figure 3.21(a), the reactive current component of the current phasor with respect to V2 voltage
decreases as highly active current is injected. This means that due to high active
current, high I2X reactive loss on the line arises, causing less reactive power at the
receiving end.
Observing the current phasor and the receiving end voltage V2 phasor in figures 3.21(b) and 3.23-(a), it is seen that current phasor has a component leading V2; which
implies that (underexcited) reactive power is absorbed from the V2 bus. This means
that, for highly (or pure) active current injection, the current phasor at the receiving end
bus takes a form of highly reactive, but as consumption (underexcited). Observing
figure 3.23-(b), when the limit is reached for pure active current, there is only reactive
56
Chapter 3 Active and Reactive Current Transfer Limits
current (underexcited) at the receiving end bus. This means that the active power
supplied by the V1 bus is consumed as I2R loss on the line, and the I2X loss (arising
with the active current flow) is absorbed from the V2 bus.
V2
X
șZ
V2
R
I limit =
I limit =
V2
Zsin(ș Z -ș I )
V2
Zsin(ș I -ș Z )
Fig. 3.24 Active/reactive current transfer limits-5.
Current magnitude limit for 270°+șZ>șI>90°+șZ (active and reactive power
consumption):
In figure 3.25, magnitude of current is increased while keeping the angle constant at șI,
where the injected current is causing active power consumption and underexcited
operation (reactive power consumption). Though such an operating point is quite
uncommon for a wind turbine during low voltage situations, transfer limits are explored
for the sake of completeness. As seen in figure 3.25, for such an injection angle, V1
drops to zero with a certain current magnitude, which is the largest current with a
possible operating point.
V2 constant
I V
2
-Z.I
T
V1
I
I=Ilimit
V2 -Z.Ilimit
TI
V1 =0
Fig. 3.25 Current magnitude limit for 270°+șZ>șI>90°+șZ
57
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
The current magnitude limit for this region of operation can be calculated as (3.14)
below.
270o +ș Z ! ș I > 90o +ș Z
Ÿ
V2 =Z.Ilimit
Ÿ
Ilimit =
V2
Z
(3.14)
The derived limit is imposed to the active/reactive current operating point plot as in
figure 3.26. The possible operating points are shown as the green-shaded area.
I limit =
TI
V2
Z
V2
X
șZ
V2
R
I limit =
I limit =
V2
Zsin(ș Z -ș I )
V2
Zsin(ș I -ș Z )
Fig. 3.26 Resultant active/reactive current transfer limits.
As seen in the resultant active and reactive current transfer limits in figure 3.26, the
valid operating points are like a band with a width depending on the receiving end
voltage (V2) and impedance magnitude (Z), and the inclination angle of the band
depending on șZ (tan-1(X/R)) of the impedance. As explained above, for any current
outside this region a valid operating point does not exist. In figure 3.27, the current
limits are drawn for a lossless (R=0) line, which is not practically existing; as seen
below theoretically no limit exists for pure reactive current for a lossless line.
58
Chapter 3 Active and Reactive Current Transfer Limits
V2
Z
V2 V2
=
Z X
ș Z =90o
Fig. 3.27 Active/reactive current transfer limits for a lossless line.
3.2.3
Summary of Current Transfer Limit Equations
Summary of the resultant current transfer limit equations are given below, such that for
a given current injection angle (active and reactive components), the maximum current
magnitude at this injection angle can be calculated, as a function of receiving end
voltage magnitude (V2) and impedance characteristics (R+jX), as below. Various ways
to define transfer limits can be derived from these equations.
­ o
o
°90 +șZ ! șI > 270 +șZ
°
șI ®
° o
o
°270 +șZ ! șI > 90 +șZ
¯
șI =90o (pure reactive) Ÿ Ilimit =
șI =0o (pure active)
Ÿ Ilimit =
șI =șZ (imp. angle)
Ÿ
Ilimit =
Ÿ
V
Ilimit = 2
Z
V2
o
Z.sin( 90 -șZ )
V2
o
Z.sin( 0 -șZ )
Ilimit =
V2
Z.sin( șZ -șI )
Ÿ
V2
Z.sin( 0o )
(3.15)
Ÿ Ilimit =
V2
Z.cos(șZ )
Ÿ
Ilimit =
V2
R
Ÿ Ilimit =
V2
Z.sin(șZ )
Ÿ
Ilimit =
V2
X
Ÿ Ilimit =
V2
Z.0
Ÿ
Ilimit =f
59
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
3.3 Correlation of Current Transfer Limits with Wind
Turbine Current Injection
In the previous sections, the current transfer limits from a bus to another bus through a
line has been derived. In order to correlate these limits with the case of current injection
from wind turbines during faults, below diagram in figure 3.28 is shown, where a WPP
is represented as a single aggregated wind turbine, with the same parameters in figure
2.2 from chapter 2.
Fig. 3.28 WPP diagram and Thevenin equivalent grid.
In case of a short-circuit fault at PCC, the current flow between WT and the faulted
location can be represented with the below single line diagram, where Z represents the
impedance between the WT terminal and faulted point (PCC), and Vf represents the
voltage at the faulted point (PCC).
Vwt TV
V f 0D
Z
R jX
Fig. 3.29 Current flow from WT to a low voltage fault.
The magnitude of the voltage at the faulted bus (PCC) mainly depends on the fault
impedance and the grid impedance (grid strength). For a severe fault, faulted bus
voltage can drop to very low values close to zero (e.g. 5%). As given in figure 3.28, the
impedance between WT and PCC is Z=0.026pu+j0.208pu. In figure 3.30, current
60
Chapter 3 Active and Reactive Current Transfer Limits
transfer limits are drawn for three different remaining voltages at PCC as 25%, 10%
and 2%, together with a WT current magnitude (1pu) circle. While applying the theory
of current transfer limits for the WPP current injection, the faulted bus voltage is
assumed to have constant magnitude during the fault. The WPP current injection
impact (boost or attenuation) on the (remaining) voltage at the faulted bus is neglected,
which is analyzed in the appendix in detail.
As observed in figure 3.30, for decreasing voltage at the faulted point (PCC), the
current transfer band becomes narrower. As summarized in table I below, when the
PCC voltage is high enough, any current can be injected since the band is wider than
WT current magnitude rating, i.e. 1pu or 1.25pu. However, when the voltage goes low,
a current within rated magnitude can be out of transfer limits for certain injection
angles. For example, when the PCC voltage is 10% as in figure 3.30-(b), pure or highly
reactive currents can be injected, whereas highly active currents cannot be injected.
Fig. 3.30 Current transfer limits for Vpcc=25% (a), Vpcc=10% (b), Vpcc=2% (c)
When the PCC voltage is very low, e.g. 2% as in figure 3.30-(c), the band becomes
almost a line and current injection angle needs to be close to the impedance angle.
61
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
Table 3.1 Current injection versus voltage magnitude at PCC
Iwt=-j1pu
Iwt=1pu
Iwt=0.86-j0.5pu
Iwt=0.12-j0.99pu
(pure reactive)
(pure active)
(highly active)
(highly reactive)
Vpcc=25%
inside limits
inside limits
inside limits
inside limits
Vpcc=10%
inside limits
out of limit
out of limit
inside limits
Vpcc=2%
out of limit
out of limit
out of limit
inside limits
Referring to the grid code FRT and reactive current injection (RCI) requirements;
assuming that the WPP shown in figure 3.28 is injecting pure reactive current of 1pu
during a low voltage fault, the maximum current that can be injected, i.e. intersection of
the transfer limit band with the reactive current axis (y-axis), depends on the resistance
value between the WT and the faulted point. In other words, the minimum faulted bus
voltage magnitude, where the WT can inject 1pu pure reactive current can be found
based on (3.10), as in (3.16) below;
șI =90o
Ÿ
I=1pu 90o =Ilimit
Ÿ
Ilimit
Vf
R
1pu
Ÿ
Vf
R pu
(3.16)
For the WPP in figure 3.28; the minimum FRT voltage levels at the PCC, for injection
of pure 1pu reactive current, are shown below for two different cases as; for the case
when the fault occurs at PCC and for the case when the fault occurs at the end of 20km
cable where the WPP is connected to the main grid. When the fault is at PCC, the
resistance of the impedance, R, between WT and the faulted point (PCC) is 0.026pu;
hence, based on (3.16), WT can inject pure reactive current of 1pu when the PCC
voltage is above 0.026pu (2.6%) as shown in figure 3.31-(a). When the fault is at the
main grid connection point (end of 20km line), the impedance, R, between WT and the
faulted point is 0.05pu. Hence, WT can inject pure reactive current of 1pu when the
voltage is above 0.05pu (5%) at the faulted bus, which results in the voltage at PCC be
observed as 10% of the rated voltage with 1pu reactive injection, as shown in figure
3.31-(b).
For the voltage sags below the values shown in figure 3.31, pure reactive current
cannot be injected by the wind turbine, irrespective of the performance and stability of
the WT control algorithms, since such an operating point does not exist. Pure reactive
62
Chapter 3 Active and Reactive Current Transfer Limits
current injection within these regions should either be avoided by some means, or
problems arising, which are studied throughout this thesis, should be considered and
solved with the proposed methods given in the following chapters of this thesis.
Fig. 3.31Minimum PCC voltage for WPP (figure 3.28) injecting 1pu pure reactive
current (a) fault at PCC (b) fault at main grid connection point.
Remark 3.11:
Observing figure 3.31 (a) and (b), it is seen that the minimum PCC voltage required for
pure 1pu reactive current injection from wind turbine is changing with the location of
the fault. As explained above; for a fault at PCC it is 2.6%, and for a fault at the end of
connection line it is 10%. Hence, for a WPP it is difficult to specify certain limits since
it is difficult to differentiate between two cases without knowing where the fault is
occurring.
The impedance between the WT and the faulted point mainly depends on the WT
transformer, WPP collector network, WPP main transformer, and connection cable (if
exists). Hence for a WPP with long collector network cables (due to distant location of
wind turbines) or a long connection cable (most likely exists for off-shore WPP)
impedance would be high and the current limit band would be narrower. It is also
important to note that, impedance between the wind turbine and the faulted point
(which might be PCC or points further towards main grid) might vary with the
temperature of the cables. It can be commented that for high wind conditions, i.e. high
power generation, cables’ resistance would increase with increasing cable temperature
63
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
due to cable loading, and the impedance characteristics would change to be more
resistive; making the limit for pure reactive current smaller.
In this section the active and reactive current limits are correlated with the WPP current
injection via taking the wind turbine bus (Vwt) as the sending end (V1) and the faulted
bus (Vf) as the receiving end (V2). However, the active/reactive current transfer limits
in this chapter are derived based on current flow between two buses, which can be any
bus, not necessarily the wind turbine bus and the faulted bus. Hence, for a case that
active and reactive currents are controlled at the PCC bus of a WPP, the limits still
apply via taking the PCC bus as the sending end and the faulted point as the receiving
end. If the fault is occurring at PCC, then the Z value between sending end (PCC) and
faulted point (again PCC) is zero and any current can be injected without limit.
However if fault is remote from PCC, for instance at the end of the connection cable
where the WPP is connected to the main grid, for pure 1pu reactive current injection at
the PCC bus, the minimum voltage at the faulted bus has to be 2.4%, due to 0.024pu
resistance of the connection cable. With 1pu reactive current injection, the voltage at
the PCC bus is observed as 9.7% in this case, as shown in figure 3.32 below.
Fig. 3.32Minimum PCC voltage for WPP (figure 3.28) injecting 1pu pure reactive
current at PCC and fault occurring at main grid connection point.
Hence, WPP level current control at PCC improves to avoid limitations of current
transfer, if fault is at PCC. However, limits still apply if the fault is remote from PCC,
which will be discussed in chapter five.
64
Chapter 3 Active and Reactive Current Transfer Limits
The minimum PCC voltages shown in figures 3.31 and 3.32 are given for pure reactive
current injection. However, as will be shown in the following chapters, if the current is
not injected as pure reactive, but with an angle close to impedance angle within the
transfer limits, then injection can be possible for lower (even zero) PCC voltage
magnitudes.
3.4 Two Operating Points Phenomenon
As observed in the derived current transfer limits in (3.15) and also in figure 3.26, a
current with magnitude smaller than Vf/Z, is always within the transfer limits, for any
current injection angle, as shown in (3.17) and blue-shaded area in figure 3.33.
I<
Vf
Z
Ÿ
I limit =
(3.17)
for 0o < șI < 360o
I<Ilimit
Vf
Vf
X
Z
șZ
Vf
R
I șI
I limit =
Vf
Zsin( ș Z -ș I )
Fig. 3.33 Resultant active/reactive current transfer limits.
Hence, any current injection from the wind turbine with magnitude smaller than Vf/Z
(in the blue-shaded area) is definitely within the transfer limits. Currents larger than
Vf/Z, can be inside (the green-shaded area) or outside the transfer limits depending on
the active and reactive combination, i.e. injection angle.
Another issue for the current larger than Vf/Z is shown in figure 3.34 and 3.35 below.
When the current magnitude is larger than Vf/Z, which means that the voltage drop on
65
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
the impedance (ZI) is larger than the receiving end Vf voltage, two operating points
exist for the same active/reactive current injection; one with șV smaller than 90° as in
figure 3.34-(a), and another one with șV larger than 90°as in figure 3.34-(b), where șV
is the phase angle difference between the Vf and Vwt voltages. As observed in 3.34 and
3.35, the operating point with șV larger than 90° results in a very low Vwt voltage,
compared to the operating point with șV smaller than 90°. In figure 3.34-(a), high active
and reactive power is supplied from Vwt (due to higher Vwt voltage) and current lags Vf
such that reactive power is supplied to the Vf point (overexcited operation); however in
figure 3.34-(b), low active and reactive power is supplied from Vwt (due to lower Vwt
voltage) and current leads Vf such that reactive power is absorbed from the Vf point
(underexcited operation). This means that when șV is larger than 90°, reactive power is
supplied from both ends (Vf and Vwt) which is dissipated on the reactance of the line
between. It is also important to note that for the operating points with șV larger than
90°, voltage at any point between WT and faulted point is smaller than any of Vf or
Vwt.
Vf constant
Vf -Z.Iconstant
Vwt
TV
TI
T I -T Z
constant
I>V /Z
constant f
Vf -Z.I constant
TV
Vwt
TI
T -T
I
Z
constant
I>Vf /Z
constant
Fig. 3.34 Two operating points with the same current; șV smaller (a) and larger (b) than
90°.
As stated above, two operating point issue is occurring for any current with magnitude
larger than Vf/Z, thus it also occurs when the current has the same angle of the
impedance as in figure 3.35. The existence of two operating points doesn’t change
current transfer limits derived in this chapter. It is only showing that for the currents in
the green-shaded area, there are two operating points for each current, which is still
inside the current transfer limits. It will be shown in following chapters that the
66
Chapter 3 Active and Reactive Current Transfer Limits
operating point with șV larger than 90° is not a stable operating point that the system
cannot stay at this operating point. It is also important to keep in mind that as seen in
the current transfer limits (figures 3.14, 3.17, 3.21, 3.23) above, at the limit points the
phase angle difference șV between Vf and Vwt reaches 90°. It will be shown that during
the loss of synchronism events, such a limit point will be reached and operating point
will become like in figure 3.34-(b) or 3.35-(b) for transients during frequency fall/rise.
Vf constant
TV
0D Vf
ș I =ș Z
constant
-Z.I
constant
Vwt
Vf
TV
-Z.I
Vwt
180D ș I =ș Z
I>V /Z
constant f
I>V /Z
constant f
Fig. 3.35 Two operating points with the same current; șV equal to 0° (a) and 180° (b).
In summary, if the current magnitude is smaller than Vf/Z, in other words inside the
blue-shaded area in figure 3.33, it is definitely inside the transfer limits, with one
operating point solution with șV smaller than 90°. However, in this case current
injection would be very small (or even zero) for severe faults and/or high impedance
cases, which would not be acceptable considering grid code requirements. For instance,
for the WPP in figure 3.28, if the current injection is kept to be smaller than Vf/Z in
order to guarantee operation within current transfer limits, for a fault at PCC with
remaining voltage of 5% the current that can be injected has a magnitude of 0.238pu
due to 0.21pu Z magnitude (0.238=0.05/0.21). Such a limited current injection scheme
will be evaluated in chapter five as a reference solution.
3.5 Conclusion
In this chapter, active and reactive current transfer limits between two buses connected
with a line are explored. It is shown that active and reactive current transfer limits do
exist similar to the active and reactive power transfer limits, which are well-known
from power system theory.
67
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
The correlation of the derived transfer limits with the WPP current injection during low
voltage faults is given. It is shown that, when the receiving end (faulted point) voltage
is very low, the current transfer limit from the sending end (e.g. wind turbine) becomes
smaller. Outside the transfer limits a “valid” operating point does not exist. The
meaning of invalid operating point and what happens if the wind turbine tries to inject a
current out of the defined transfer limits will be analyzed in the next chapter.
It is important to note that the active and reactive current transfer limits derived here is
exploring an underestimated phenomenon for wind turbines’ current injection during
low voltage faults, which has been omitted in the wind power studies before. In the
previous studies, it has been assumed that the wind turbine can inject any controlled
current from its terminals irrespective of the fault level at the PCC. However, as shown
in this chapter, limits apply due to low voltage at the grid side and due to the
impedance between WT and PCC, and some currents “cannot” be injected. The theory
of current limits derived in this chapter will be verified with simulation and experiment
results in the following chapters.
It should be noted that the transfer limits derived in this chapter are “steady-state”
limits, such that the limits can be exceeded during short-time transients. It is important
to realize that any current out of the defined transfer limits cannot be flowing, which
means that there is not any operating point out of the transfer limits in steady-state
period of a low voltage fault.
The derived current limits can be utilized for other applications, such as current
injection from a STATCOM to a low voltage bus, or HVDC or WPP current injection
to a weak grid, including non-faulted operation (when the grid side voltage is at rated).
The derived current transfer limits are based on phasor theory; hence can be applied for
positive sequence voltages and currents, but also for negative sequence and zero
sequence as well.
68
Chapter 3 Active and Reactive Current Transfer Limits
69
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
Chapter 4
Analysis of Loss of Synchronism (LOS) during
Symmetrical Faults
In this chapter, Loss of Synchronism (LOS), which was identified in chapter 2, is
analyzed. The correlation of LOS occurrence with the active and reactive current
transfer limits, which have been derived in chapter 3, is shown. The reasons and
dynamics of LOS - frequency fall and rise events during low voltage faults are explored
with large-signal and small-signal stability analysis, verified with EMT simulations
and experimental results of a grid-connected converter.
4.1 Correlation of Observed LOS and Current Transfer
Limits
The active and reactive current transfer limits have been derived in chapter 3. It is
shown that, especially for severe symmetrical faults, where the grid voltage drops down
close to zero, and for high impedance between the WT and the faulted point (e.g. PCC),
strict current transfer limits exist. However it is known that, these transfer limits, which
sets dependency between active and reactive current components, have not been
considered within conventional control methods. Hence, while the WPP is injecting
active and reactive currents during low voltage faults based on conventional control
methods, the referenced currents may easily be out of the transfer limits, which might
cause LOS events shown in chapter 2. In order to see the relation between LOS events
in chapter 2 and the current transfer limits in chapter 3, figure 4.1 is given. In figure
4.1, the transfer limits in figure 3.30 are imposed on the results from figure 2.7. As seen
in figure 4.1, the observed LOS events are consistent with the transfer limits, such that
70
Chapter 4 Analysis of Loss of Synchronism during Symmetrical Faults
the LOS events are occurring for cases 1, 3, and 6 where the current references are out
of the transfer limits (green-shaded areas).
I wt =I ș I =1pu 90o
ș I =90
ș I =83
o
ș I =90
I wt =I ș I =1.01pu 83o
o
ș I =90
ș I =83
o
I wt =I ș I =1.2pu 57o
o
ș I =57
o
ș I =83
o
ș I =57
o
o
ș I =57
o
Fig. 4.1 Correlation of Observed LOS and Current Transfer Limits.
The LOS events in this study are observed when the current references are out of the
current transfer limits, such that the WT is referenced to operate at a point where a
valid operating point does not exist. An analogy can be given from classical power
71
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
system theory; such that the conventional synchronous generator accelerates during a
low voltage fault if the synchronous generator is given an input mechanical power
higher than the electrical power transfer limit.
4.1.1
Response of WT to Non-transferrable Current Reference
As shown in active and reactive current transfer limits between two buses in chapter 3,
when the receiving end (PCC) voltage is very low (e.g. 2%) the active and reactive
current flow is mainly dictated by the X/R ratio of the impedance between the two
buses. Based on figure 3.11 and (3.9), when the receiving end voltage is very low (e.g.
smaller than 2%), the transferrable current has the angle of the impedance between two
buses (between WT and PCC bus).
Vf | 0
Ÿ
Iactive R
=
Ireactive X
Ÿ
șI =șZ
(4.1)
In such a severe fault case the WT current angle is dictated by the grid impedance
irrespective of the referenced current; in other words the grid dictates the current to stay
within the band of the current transfer limits. Hence, active and reactive current
references cannot be realized. The simulation case from chapter 2, figure 2.2 is
executed again for a severe fault occurring at PCC point, where the PCC voltage drops
to 1% of the rated. It should be remembered that in this case the impedance between
WT and PCC had X/R ratio of 8, which implies an impedance angle of 83°. The case,
with pure reactive current reference, is shown in figure 4.2 below. As observed in
second subfigure, active and reactive current references are realized. However, the
measured active and reactive current references are calculated based on the angle
estimated by the PLL. In order to see the actual active and reactive current components,
phase-“a” voltage and current are shown in third subfigure. Around time equal to 1.06
second, where the WT operates at a quasi stationary point around 45Hz, the zero
crossing time difference between phase-“a” voltage and current is found to be 5
millisecond, which implies that the phase difference of 81°. Even though the angle of
the current reference was given as 90°, the actual current is dictated by the grid to be
inside the current transfer band. In the fourth subfigure, the Vd and Vq signals within
the PLL are shown. As known, the PI compensator of the PLL acts on the error, the Vq
72
Chapter 4 Analysis of Loss of Synchronism during Symmetrical Faults
signal, to lock the measured voltage to Vd, i.e. d-axis. As seen in fourth subfigure,
before the fault at time equal to 1 second, PLL is able to keep the Vq signal at zero,
which means that the estimated angle is correct. However, during the fault, there occurs
a sustained (negative) Vq error, which cannot be compensated. Thus, the current
regulator is able to realize the current reference with respect to the estimated d&q axes
but the estimated d&q axes by PLL are incorrect. It should be noted that the sustained
estimation error of the PLL arises due to the given current reference, which is out of the
current transfer limits. The referenced current and the transfer limits are shown in
figure 4.4-(a), and the resultant quasi steady-state phasor diagram showing actual
current phasors together with the referenced and transfer limits is given in figure 4.4(b).
The results of case with 1pu reactive end 0.65pu active current reference during a
severe fault at PCC, where the voltage drops to 1% of the rated, is given in figure 4.3.
Similar to the previous case, the referenced active and reactive currents cannot be
realized and the actual current angle is observed as 85°, though the reference is 57°. A
sustained (positive) Vq signal, i.e. PLL error, is observed during the fault. The
referenced current and the transfer limits are shown in figure 4.5-(a), and the resultant
actual current phasors together with the referenced and transfer limits are shown in
figure 4.5-(b).
It is shown that a current reference out of the transfer limits causes a sustained PLL
estimation error. When the sustained estimation error is continuously integrated by the
integrator of the PLL, a fall or rise of frequency is observed as in chapter 2 and here.
As discussed in section 2.2.6, in practical saturation is applied for the integrator and
calculated frequency within the PLL. However, limiting the frequency to a value (e.g.
45Hz or 55Hz) doesn’t change the fact that the sustained estimation error occurs. In the
next chapter implementation of the saturation and anti-windup algorithms for the PLL
and impact will be evaluated.
73
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
It should be kept in mind that, the sustained estimation error arises due to the current
reference out of the transfer limits. Hence, the LOS is an issue related to the
“inconvenient” active and reactive current references and causes loss of control of
active and reactive currents, i.e. loss of vector control.
Vpcc-abc&rms
(pu)
1
Vpcc-a
Vpcc-b
Vpcc-c
0.5
0
-0.5
-1
Iwt Active&Reactive
(pu)
0.9
0.92
0.94
0.96
0.98
1
1.02
1.04
1.06
1.08
1.1
1.12
1.14
1
1.16
1.2
Ireact - ref
Ireact - meas
Iact - ref
Iact - meas
0.5
0
0.9
0.92
0.94
0.96
0.98
1
1.02
1.04
1.06
1.08
1.1
1.12
1.14
1.16
1
Vwt-a& Iwt-a
(pu)
1.18
1.18
1.2
Vwt-a
Iwt-a
0.5
0
X: 1.056
Y: 0.002487
-0.5
X: 1.061
Y: 0.005335
-1
0.9
0.92
0.94
0.96
0.98
1
1.02
1.04
1.06
1.08
1.1
1.12
1.14
1.16
Vd-pll & Vq-pll
(normalized)
1
1.2
Vd-pll
Vq-pll
0.5
0
0.9
0.92
0.94
0.96
0.98
1
1.02
1.04
1.06
1.08
1.1
1.12
1.14
50
WT frequency
(Hz)
1.18
1.16
1.18
1.2
WT frequency
45
40
X: 1.059
Y: 43.24
35
30
0.9
0.92
0.94
0.96
0.98
1
1.02
1.04
1.06
time (s)
1.08
Fig. 4.2 WT response during LOS – frequency fall event.
74
1.1
1.12
1.14
1.16
1.18
1.2
Chapter 4 Analysis of Loss of Synchronism during Symmetrical Faults
Vpcc-abc&rms
(pu)
1
Vpcc-a
Vpcc-b
Vpcc-c
0.5
0
-0.5
-1
Iwt Active&Reactive
(pu)
0.9
0.92
0.94
0.96
0.98
1
1.02
1.04
1.06
1.08
1.1
1.12
1.14
1
1.16
0
0.92
0.94
0.96
0.98
1
1.02
1.04
1.06
1.08
1.1
1.12
1.14
1.16
Vwt-a& Iwt-a
(pu)
1
1.18
1.2
Vwt-a
Iwt-a
0.5
0
-0.5
X: 1.108
Y: -0.007885
X: 1.111
Y: -0.009231
1.08
1.12
-1
0.9
Vd-pll & Vq-pll
(normalized)
1.2
Ireact - ref
Ireact - meas
Iact - ref
Iact - meas
0.5
0.9
0.92
0.94
0.96
0.98
1
1.02
1.04
1.06
1.1
1.14
1.16
1
1.18
1.2
Vd-pll
Vq-pll
0.5
0
0.9
0.92
0.94
0.96
0.98
1
1.02
1.04
1.06
1.08
1.1
1.12
1.14
100
WT frequency
(Hz)
1.18
1.16
1.18
1.2
WT frequency
80
X: 1.109
Y: 78.61
60
0.9
0.92
0.94
0.96
0.98
1
1.02
1.04
1.06
time (s)
1.08
1.1
1.12
1.14
1.16
1.18
1.2
Fig. 4.3 WT response during LOS – frequency rise event.
75
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
ș pll-error
Vwt
*
șI
*
șI
D
ș Z =83
D
ș I =81
I*wt =I wt
I*wt
Fig. 4.4 Current transfer limits and (a) pure reactive reference current phasor, (b) WT
voltage and actual current – causing sustained negative PLL error and LOS frequency
fall.
D
ș Z =83
ș I =85
D
Vwt
ș pll-error
*
șI
I*wt
*
șI
I*wt =I wt
Fig. 4.5 Current transfer limits and (a) highly active reference current phasor, (b) WT
voltage and actual current – causing sustained positive PLL error and LOS frequency
fall.
Based on the current transfer limits, an equation for the change of frequency of the WT
can be obtained empirically as below, where Ki is the integral gain of the PLL. The Vq
signal magnitude disappears with the use of the normalization block for measured
phase voltages in the PLL.
dfwt
=Ki Vq =Kisin(șpll-error )=Kisin(șZ -ș*I )
dt
76
(4.2)
Chapter 4 Analysis of Loss of Synchronism during Symmetrical Faults
4.2 Large-Signal Stability Analysis of PLL during LOS
The analysis of the LOS is done using the WPP structure in figure 4.6 below, which is
aggregated as a single wind turbine and used in the previous cases. As done in the
previous cases, a symmetrical severe fault at PCC point (alternatively at the point
where the WPP is connected to the main grid) is considered.
Fig. 4.6 WPP structure used in large-signal stability analysis.
Voltage at the faulted point (e.g. PCC) is assumed to be constant (i.e. constant Vf) and
the impedance between the wind turbine and the faulted point is represented as Z
(R+jX) as shown in figure 4.7. In this case the grid-side voltage becomes the faulted
point voltage Vf with phase angle șf.
Vf ɽf
Vwt ɽwt
Z
R jX
Fig. 4.7 Current injection during fault.
Based on the separation principle the voltage at the wind turbine terminal Vwt, where
the phase voltages and currents are measured for feedback to PLL and current control,
can be obtained as superposition of two sources; the grid side (faulted point) voltage Vf
77
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
and the current injection by the wind turbine, as shown in figure 4.8, similar to the
approach in [79]. The saturation blocks, which were shown in PLL structure in figure
2.10, are not shown for simplicity in this case.
VwtͲf
VwtͲI
Iwt ɽI
Z ɽZ
VwtͲI
VwtͲf
Vf ɽf
Z ɽZ
vq
vd
Fig. 4.8 Wind turbine voltage during fault as superposition of two sources [79].
The wind turbine feedback voltage can be written as composition of two voltages as in
(4.3) to (4.5) below;
Vwt =Vwt-I Vwt-f
(4.3)
Vwt-I =Z șZ ˜ Iwt șI
(4.4)
Vwt-f =Vf șf
(4.5)
The phasor diagram showing the active and reactive current injection, together with
wind turbine and faulted point voltages is given in figure 4.9.
78
Chapter 4 Analysis of Loss of Synchronism during Symmetrical Faults
Vwt
Z.I
T wt
T Z -T I
I
Vf
Tf
T I TV
Fig. 4.9 Phasor diagram showing wind turbine voltage, current and fault point voltage.
The q-axis component of the wind turbine voltage, which is error input of the PI
compensator within PLL, can be written in terms of the q-axis components of the two
sources; grid-side (faulted point) voltage and the voltage drop on the impedance due to
the injected current (ZI), as in (4.6) to (4.8);
Vq =sin(șV ) ˜ Vf
(4.6)
Vq+ =sin(șZ șI ) ˜ Z ˜ Iwt
(4.7)
Vq =Vq Vq
(4.8)
The grid angle reference that is tracked in this case is the angle of the faulted pointed
voltage, which represents the grid voltage in the faulted network, and the frequency of
the main grid is the frequency at the faulted point. The mathematical model of the PLL
for a quasi-stationary operating point, where the grid (faulted point) frequency Ȧf, and
wind turbine frequency, Ȧwt, can have different values (due to possible LOS), is shown
in figure 4.10 below [79]. The feedback sourcing from the grid (faulted point) voltage
Vq- provides the necessary negative feedback for the PLL to track the grid phase angle
șg, which is șf in the faulted case. However, the feedback sourcing from the current
injection,Vq+, behaves as a positive feedback, which can be considered as a disturbance
to the stability of the PLL. The angle and magnitude of the impedance Z is taken as a
79
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
function of the wind turbine frequency. The angle of the injected current, șI, is based on
the active and reactive current magnitudes and independent of the wind turbine
frequency.
v q
v q
vq
Fig. 4.10 Quasi-stationary model of the PLL [79].
The large signal stability of the PLL requires a negative feedback magnitude larger
than the positive feedback as given in (4.9) and (4.10);
Vq > Vq
(4.9)
Vf sin(șV ) ! ZIwt sin(șZ șI )
(4.10)
The constraint for current magnitude can be written as in (4.11) for șV equal to ±90°;
Vf
Zsin (șZ șI )
! Iwt
(4.11)
It is interesting to see that the large-signal stability limit for the PLL is found to be the
same as the current transfer limits from chapter 3, figure 3.26 and equation (3.15). As
also seen in (4.10), large-signal stability depends on the current injection angle șI, such
that injection angle same as impedance angle reduces the positive feedback component
(Vq+) to zero, providing stability. The global large-signal stability requirement is given
in (4.12), which is the counterpart of the blue-shaded circle in figure 3.33 in chapter 3,
such that when the voltage drop on the impedance is smaller than the faulted point
voltage magnitude, stability is provided for any injection angle.
Vf
! Iwt
Z
(4.12)
As observed in (4.10) and phasor diagram in figure 4.9 above, the large-signal stability
limit is reached when șV reaches ±90°; similar to the cases in chapter 3 (figures 3.14,
80
Chapter 4 Analysis of Loss of Synchronism during Symmetrical Faults
3.17, 3.21, 3.23). As observed in the previous cases, a frequency deviation (fall or rise)
from the main grid (faulted point) frequency during a LOS implies that the angle
difference șV goes beyond ±90° and causes phase jumps at the wind turbine voltage
with respect to the faulted point voltage.
It will be shown in the following parts with small-signal stability analysis that the
instability can also be observed before șV reaches ±90°, due to sensitivities for the
operating points with șV close to ±90°.
For the current magnitudes causing large-signal instability, which are found to be the
same as current transfer limits, LOS occurs as observed in previous cases. During the
LOS, the positive feedback magnitude becomes larger than the negative feedback
magnitude causing sustained PLL error Vq. As discussed in the preceding section
compensation (proportional plus integration) of sustained error causes deviation of the
wind turbine frequency. Based on the sustained error magnitude, neglecting the
negative feedback (due to low Vf) and the transient contribution from the proportional
compensator, the rate of change of frequency is calculated as below;
Vq =Vq Vq+ =Vf sin(șV ) ZIwt sin(șZ șI )
Ȧwt =2ʌ50+(Kp +
Ki
)Vq
s
dȦwt
=Ki Vq =Ki ZIwt sin(șZ șI )
dt
(4.13)
(4.14)
(4.15)
Approximating the Vwt voltage magnitude as the voltage drop on the impedance, ZI, for
very low fault voltages, the Vq signal is divided by ZI magnitude due to the
normalization function within PLL, in figure 4.8, yielding the rate of change of
frequency as;
dȦwt
=Ki sin(șZ șI )
dt
(4.16)
For the case in figure 4.2 (case-1 in figure 2.4), where the current reference was given
as 90° to an impedance of 83°, the rate of change of frequency (with a PLL Ki of 3000)
is calculated to be around -58Hz/sec, which can also be seen in figure 4.2.
81
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
dfwt Ki sin(șZ șI ) 3000u sin(83 90)
58Hz / sec
=
dt
2S
2S
(4.17)
It is important to note that during LOS-frequency fall, the impedance characteristics
(magnitude and angle) change considerably due to change of frequency. Since the
frequency is falling towards zero the reactance component (X) magnitude decreases
towards zero, causing the impedance to become pure resistance with zero angle
(șZ(Ȧwt)=0°); which in turn increases error magnitude causing exponentially increasing
of rate of change (fall) of frequency. Similarly for the case in figure in 4.3 (case-3 in
figure 2.6), where the current reference was given as 57° to an impedance of 83°, the
rate of change of frequency (with a PLL Ki of 3000) is calculated to be around
+209Hz/sec.
dfwt Ki sin(șZ șI )
=
dt
2S
3000 u sin(83 57)
209Hz / sec
2S
(4.18)
In this case rise of frequency cause the impedance to become pure reactance
(șZ(Ȧwt)=90°), again causing exponentially changing frequency. Rate of change of
frequency value gives the chance to evaluate the impact of a LOS event during a low
voltage fault. For instance, for the cases given previously, considering typical fault
duration of 150ms, the frequency would deviate around -9Hz for the fall event and
31.5Hz for the rise event. This implies that a considerable frequency deviation would
occur, which should be avoided by solutions as will be given in the following chapters.
Such a rate of change of frequency can represent the “inertia” of the wind turbine
during LOS event, and would be beneficial to analyze how fast the LOS and frequency
deviation would occur.
4.3 Experimental Verification of the Simulation Results
In this section, a grid-connected converter, which is representing an aggregated WPP
and injecting active/reactive current during a low voltage fault, is experimentally
investigated. The experimental setup is shown in Figure 4.11 below. The converter’s dc
side is connected to a dc power supply, with 650Vdc. The current transfer limits and
LOS are verified based on the remaining voltage at the faulted point and the impedance
between the controlled point (WT) and the faulted (PCC) point. The PLL is
82
Chapter 4 Analysis of Loss of Synchronism during Symmetrical Faults
implemented with a saturation limit, which is kept high as 0Hz minimum and 60Hz
maximum, in order observe the frequency fall/rise during LOS substantially. Three
cases are created similar to the cases 1 to 3 in chapter 2 and section 4.1. In case-1 pure
reactive current, in case-2 a combination of active and reactive current, and in case-3
high active current is injected by the converter. As seen in Figure 4.11, the
experimental setup has relatively low impedance magnitude (Z=0.018pu+j0.036pu)
with a low X/R ratio of 2 (șZ=63°) between the WT terminal and the PCC, where the
fault is created.
Fig. 4.11 Experimental setup.
The voltage sag at the bus called as PCC is created by use of the autotransformer,
which can drop the voltage down to 0.01pu (1% of the rated).
In the experimental case-1, shown in Figure 4.12, pure 1pu reactive current is
referenced to the wind turbine when the voltage sag is created at time equal to 2.2
second. As expected, LOS – frequency fall occurs, similar to the simulation case-1
(figure 2.4) in chapter 2. As seen in first subfigure, the vector control algorithm is
realizing the active and reactive current references, with respect to the angle estimated
by the PLL. However, as explained in above parts, PLL estimation is incorrect as also
83
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
seen in third subfigure that the Vq component remains as a non-zero negative value
during the current injection. Due to the sustained PLL error, negative Vq, the frequency
calculated by the PLL, thus frequency of the voltage and current generated by the
converter, falls down to zero (dc).
In the experimental case-2, shown in Figure 4.13, current reference with 0.375pu active
and 0.75pu reactive components, which are having the same ratio as X/R ratio of the
impedance, is given to the wind turbine at time equal to 3.15 second. The current
reference and the impedance have the same angle of 63°. Hence, LOS does not occur
and converter stays synchronized at 50Hz, similar to the simulation case-2 (figure 2.5)
in chapter 2. As seen in third subfigure, the PLL error Vq is kept around zero in this
case.
In the experimental case-3, shown in Figure 4.14, the WT has 1pu active current
reference and 1pu reactive current is referenced when the voltage sag is created at time
equal to 2.75 second, causing highly active current reference, which has angle of 45°,
smaller than the impedance angle of 63°. As expected, LOS – frequency rise occurs,
similar to the simulation case-3 (figure 2.6) in chapter 2, since the current reference
angle is lower than impedance angle. As seen in first subfigure, the vector control
algorithm is realizing the active and reactive current references, with respect to the
angle estimated by the PLL. However, as explained in above parts, PLL estimation is
incorrect during LOS, as also seen in third subfigure that the Vq component remains as
a non-zero positive value during the LOS. Due to the sustained PLL error, positive Vq,
the frequency calculated by the PLL, thus frequency of the voltage and current
generated by the converter, rises towards 60Hz.
84
Chapter 4 Analysis of Loss of Synchronism during Symmetrical Faults
Vwt-a & Iwt-a
(pu)
Iwt Active&Reactive
(pu)
1
0
1.5
Vd-pll & Vq-pll
(pu)
2
2.5
3
1
3.5
Vwt-a
Iwt-a
0
-1
1.5
WT frequency
(Hz)
Ireact - ref
Ireact - meas
Iact - ref
Iact - meas
0.5
2
2.5
3
3.5
0.3
Vd-pll
Vq-pll
0.2
0.1
0
1.5
50
40
30
20
10
0
1.5
2
2.5
3
3.5
WT frequency
2
2.5
time (s)
3
3.5
Fig. 4.12 Experimental case-1: Loss of Synchronism – Frequency Fall.
Based on (4.15), the rate of change of frequency is calculated as -150Hz/sec, as also
observed in Figure 4.12.
dfwt Ki Vq Ki sin(șZ șI )
=
=
dt
2S
2S
2000u sin(63 90)
150Hz / sec
2S
(4.19)
85
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
Iwt Active&Reactive
(pu)
1
Ireact - ref
Ireact - meas
Iact - ref
Iact - meas
0.5
0
-0.5
2.5
3
3.5
4
Vwt-a & Iwt-a
(pu)
1
4.5
Vwt-a
Iwt-a
0.5
0
-0.5
-1
2.5
3
3.5
4
4.5
Vd-pll & Vq-pll
(pu)
0.06
Vd-pll
Vq-pll
0.04
0.02
0
-0.02
2.5
3
3.5
4
4.5
WT frequency
(Hz)
55
WT frequency
50
45
2.5
3
3.5
time (s)
4
Fig. 4.13 Experimental case-2: Stable operation – synchronized to 50Hz.
86
4.5
Chapter 4 Analysis of Loss of Synchronism during Symmetrical Faults
Vwt-a & Iwt-a
(pu)
Iwt Active&Reactive
(pu)
1
-1
1.5
Vd-pll & Vq-pll
(pu)
2
2.5
3
1
3.5
Vwt-a
Iwt-a
0
-1
1.5
WT frequency
(Hz)
Ireact - ref
Ireact - meas
Iact - ref
Iact - meas
0
2
2.5
3
0.3
3.5
Vd-pll
Vq-pll
0.2
0.1
0
1.5
2
2.5
3
3.5
65
60
55
50
45
1.5
WT frequency
2
2.5
time (s)
3
3.5
Fig. 4.14 Experimental case-3: Loss of Synchronism – Frequency Rise.
Based on (4.15), the rate of change of frequency is calculated as +100Hz/sec, as also
observed in Figure 4.14.
dfwt Ki Vq Ki sin(șZ șI )
=
=
dt
2S
2S
2000 u sin(63 45)
100Hz / sec
2S
(4.20)
87
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
4.4 Small-Signal Stability Analysis within Transfer Limits
Small-signal stability of a system is a measure of its stability against small-signal
disturbances, when the system is operating at a steady-state point. Hence, small-signal
stability of the WT can be analyzed if the WT is at a valid operating point. However, as
discussed above, the LOS events in this study are observed (cases 1, 3, and 6) when the
current references are out of the current transfer limits, such that the WT is referenced
to operate at a point where a valid operating point does not exist, which is shown to
cause large-signal stability. Hence, small-signal stability analysis cannot be conducted
for the LOS cases 1, 3, and 6. However, the non-problematic cases with current
references within the transfer limits (cases 4, 5, 7, 8, and 9) are shown to be operating
stable. It is shown that using the generic current regulator and grid synchronization
(PLL) structures and tuning them in accordance with the grid and wind turbine
performance requirements, the wind turbine is able to inject current references when
the references are within the transfer limits. As known from literature, small-signal
stability of the wind turbine is a concern when the grid voltage is very low and/or the
grid impedance is high (weak grid). Also, as will be seen in the next chapter, some of
the proposed solutions in this thesis are based on modifying the current references to be
inside the transfer limits. Hence, it is beneficial to analyze small-signal stability of the
wind turbine for current injection within the transfer limits. It should be kept in mind
that even though the wind turbine has small-signal stability for the current references
within the transfer limits, the wind turbine inevitably experiences LOS when referenced
currents are out of the transfer limits.
The model in figure 4.10 is utilized for small-signal stability analysis, as done in [79].
In this study, small-signal stability analysis is done only for the faulted case without
any local loads at PCC, where the fault is occurring at PCC, as shown in figure 4.6
above. The large-signal negative and positive feedback terms are linearized at an
operating point (with current injection within transfer limits) and at an operating
frequency (of the wind turbine), Ȧop, to reach small-signal model. The negative
feedback terms are linearized as below;
88
Chapter 4 Analysis of Loss of Synchronism during Symmetrical Faults
Vq =Vf sin(șV )
(4.20)
=V cos(ș )
V
q
f
V
(4.21)
The șV angle at the operating point can be obtained by solving the below equality based
on current injection magnitude (Iwt) and angle (șI).
Vf sin(șV )=Iwt Z sin(șZ șI )
(4.22)
It is important to note that, when the difference between impedance angle (șZ) and
current angle (șI) increases, the phase angle difference (șV) between wind turbine
voltage and faulted point voltage increases, such that 90° the transfer limit is reached.
Due to cosine term in (4.21), operating points with șV larger than 90° result in a
negative gain at the negative feedback of the PLL, which will be shown to cause
instability. The positive feedback terms are linearized as below;
Vq+ =Iwt Z(Ȧwt ) sin(șZ (Ȧwt )-șI )
(4.23)
=I ª Z(Ȧ ) +k Ȧ
¼ sin( șZ (Ȧwt )-șI +kșȦ
wt )
V
q+
wt ¬
wt
Z wt º
(4.24)
=I ª Z(Ȧ ) +k Ȧ
º ªsin( șZ (Ȧwt )-șI )+kș Ȧ
wt º
V
q+
wt ¬
wt
Z wt ¼
¬
¼
(4.25)
kZ =
kș =
ı Z(Ȧwt )
ıȦwt
=
ı R2 +(Ȧwt L)2
ıȦwt
Ȧwt =Ȧop
ı șZ (Ȧwt )-șI
ıȦwt
Ȧwt =Ȧop
=
Ȧwt =Ȧop
§Ȧ L·
ıtan-1 ¨ wt ¸
© R ¹
=
ıȦwt
L2Ȧop
R2 +(Ȧop L)2
=
Ȧwt =Ȧop
L2Ȧop
=
(4.26)
Z(Ȧop )
L
2
§ § Ȧop L ·
R ¨1+ ¨
¨ © R ¸¹
©
·
¸
¸
¹
=
RL
Z(Ȧop )
2
(4.27)
The operating point frequency Ȧop is taken as fundamental frequency (50Hz) in the
calculations in this section.
=I ª Z(Ȧ ) k +sin( ș (Ȧ )-ș )k º Ȧ
wt =Iwt K+FBȦ
wt
V
q+
wt ¬
op
ș
Z
op
I
Z
¼
(4.28)
K
+FB
89
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
Substituting kz and kș from (4.26) and (4.27) into (4.28), the positive feedback gain
term (4.29) is obtained;
K+FB = Z(Ȧop )
RL
Z(Ȧop )
+sin( șZ (Ȧop )-șI )
2
L2Ȧop
Z(Ȧop )
L
R+sin( șZ (Ȧop )-șI )LȦop (4.29)
Z(Ȧop )
=
The small-signal model of the PLL is obtained as in figure 4.15 below [79]. As stated
above, for șV larger than 90° the negative feedback gain gets negative value, causing
small-signal instability as shown below. The transfer function at the operating point
around fundamental frequency (50Hz) is obtained as in (4.30).
s Kp cos(șV )Vf s+Ki cos(șV )Vf wt
Ȧ
= 2
ș
s (1 Kp Iwt K+FB ) s Kp cos(șV )Vf Ki Iwt K+FB Ki cos(șV )Vf
g
ɽ
ɽ g wt
v q
v q
v q
ɽI
(4.30)
ʘ wt
ɽ wt
ɽZ (ʘop )
ʘ wt
Fig. 4.15 Small-signal model of PLL [79].
The transfer function in (4.30) can give measure of frequency behavior during a fault
with current injection from wind turbine against a small disturbance in the grid phase
angle (e.g. as a result of a load disconnection on the grid side). Based on the
characteristic equation in the denominator of the transfer function in (4.30), the smallsignal stability criteria can be obtained as in (4.31);
K cos(ș
p
V
)Vf Ki Iwt K+FB (1 Kp Iwt K+FB )
!0
(4.31)
Assuming that the wind turbine current is around 1pu and the proportional constant Kp
is not larger than 1/K+fb, the denominator in (4.31) is positive; yielding the stability
criteria in (4.32), which is expanded as in (4.33);
90
Chapter 4 Analysis of Loss of Synchronism during Symmetrical Faults
K p cos(șV )Vf > Ki Iwt K +FB
Kpcos(șV )Vf > Ki Iwt
L
Z (Zop )
(4.32)
R sin( ș (Z
Z
op
) șI )LZop
(4.33)
Interpreting (4.33), it can be commented that for higher Vf values, or smaller current
magnitudes, stability can be provided easily, as same was also commented in chapter 3
with the current transfer limits approach. It is important to note that when the current
injection angle is same as the impedance angle, the second term on the right hand side
of (4.33) is eliminated but still small-signal instability can occur depending on the
controller gains, fault voltage and impedance characteristics. When the current angle
deviates from the impedance angle, șV angle increases as given in (4.22); thus the right
hand side term increases due to the sine term and left hand side term decreases due to
the cosine term, which in turn increases risk of instability. In other words, for
increasing deviation of the current angle from the angle of the impedance, the angle
difference between WT voltage and faulted voltage, șV, increases (refer figure 4.17);
increasing small-signal instability risk, and moves towards ±90° to the current transfer
limit (i.e. large-signal instability). As stated above, for any operating point with șV
larger than ±90° the left hand side term gets negative values causing small-signal
instability, such that the wind turbine cannot operate with this angle as stated in chapter
3.
For the system given in figure 4.6 closed-loop poles are calculated for different
operating points, with varying current injection angle, for a PCC voltage of 0.05pu. The
results are given in table 4.1 below. It should be noted that the case with șV equal to 95°
can only be obtained with a current magnitude larger than Vf/Z, as discussed in chapter
3. As seen in table 4.1, unstable poles in right half-plane are observed when the current
angle deviates from impedance angle and șV increases towards ±90°.
91
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
Table 4.1 Poles calculated for different operating points
Vf=0.05pu, Iwt=1pu, Z=0.21pu, șZ=83° (X/R=8)
șI
resulting șV
poles
82.9°
0°
s1,2= –17.8162 ± 18.3067i
89.8°
-30°
s1,2= –16.3310 ± 18.8402i
76°
30°
s1,2= –16.3310 ± 18.8402i
69.15°
85°
s1,2= – 0.0652 ± 9.1803i
69.12°
87°
s1,2= 0.8954 ± 7.0977i
69.1°
90°
s1= 0.4, s2= 4.25
69.15°
95°
s1= –6.2, s2= 17
The nine cases given in chapter 2 and 4 are summarized in table 4.2 for their smallsignal stability analysis results with the calculated closed-loop poles. The nonproblematic cases in figure 4.1 are shown to have stable closed-loop poles, as expected.
Table 4.2 Poles calculated for cases in figure 4.1
Z=0.21pu, șZ=83° (X/R=8)
resulting șV
poles
N/A
large-signal instability
1.01pu 83o
0°
s1,2= –7.7529 ± 15.4046i
0.02
1.2pu 57o
N/A
large-signal instability
4
0.05
1pu 90o
-15°
s1,2= – 17.6012 ± 18.5918i
5
0.05
1.01pu 83o
0°
s1,2= – 17.8162 ± 18.3067i
6
0.05
1.2pu 57o
N/A
large-signal instability
7
0.25
1pu 90o
-6°
s1= –80.3, s2= –23.2
8
0.25
1.01pu 83o
0°
s1= –77.2, s2= –23.3
9
0.25
1.2pu 57o
26°
s1= –96.7, s2= –22.7
Vpcc (pu)
1
0.02
1pu 90o
2
0.02
3
92
I șI
Case
Chapter 4 Analysis of Loss of Synchronism during Symmetrical Faults
In figure 4.17, root loci for varying șV are given for the system in figure 4.6. As
observed in table 4.1, the closed-loop poles (ı+jȦd) move to the right-half plane
causing small-signal instability for increasing șV angle. Not being shown here, the root
loci change considerably with the faulted point (PCC) voltage, such that for lower (e.g.
0.02pu) faulted point voltage cases, closed-loop poles move towards the right-half
plane increasing the risk of small-signal instability.
Im(s1,2 )
(Zd )
20
X: 0.07748
Y: 8.909
10
Re(s1,2 )
attenuation
(9Zn )
0
-10
X: 0.07748
Y: -8.909
-20
-20
-10
0
10
20
ɽV (degrees)
90
X: 0.07748
Y: 85.3
60
30
Re(s1,2 )
attenuation
(9Zn )
0
-30
-60
X: 0.07748
Y: -85.3
-90
-20
-10
0
10
20
Fig. 4.16 Root loci for varying șV, for Vf =0.05pu, for system in figure 4.6.
93
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
From figure 4.17 and previous discussions, it can be commented that the system
becomes unstable before șV reaches ±90°, which is the large-signal stability limit.
Hence, within the current transfer limits, small-signal stability limits exist due to
sensitivities for operating points close to ±90°. This statement is shown in figure 4.17,
where the deviation of the current angle from the impedance angle is projected to the
deviation of the wind turbine voltage from the reference voltage (Vf). As seen in figure
4.17, a small-signal stability limit can be applied within the current transfer limits,
based on a desired value of damping and attenuation value. Additionally, the smallsignal stability margin of the system can be improved via designing and tuning the PLL
of the system accordingly. As will be seen in the next chapter, in this study stability of
the wind turbine is aimed via modifying the current references to be within transfer
limits to avoid LOS occurrence. Large-signal instability limit is considered and such a
small-signal stability limit is not applied. However the small-signal model given in this
section will be utilized for design and tuning of the frequency based controller in the
next chapter.
Vf
X
Vf
R
Fig. 4.17 Small-signal stability limit – representative attenuation values.
94
Chapter 4 Analysis of Loss of Synchronism during Symmetrical Faults
The LOS frequency fall/rise can be explained in various ways. As explained in chapter
3, during very low voltage faults the current from the wind turbine has to be injected
convenient to the angle of the impedance between the wind turbine and the faulted
point (e.g. PCC). Otherwise the active and reactive power losses on the impedance are
not compensated effectively, which is the basis of the current transfer limits, and LOS
occurs. In another explanation, an inconvenient current reference (highly active or
highly reactive out of the transfer limits) drives the angle difference between the wind
turbine voltage and the faulted point, șV, beyond ±90°, which is the basis of the largesignal stability limit, and LOS occurs; such that the frequency falls (or rise) causing the
șV decrease (or increase) with respect to the reference angle continuously.
Two cases with șV larger than ±90° should not be mixed; as explained in chapter 3, for
currents within the transfer limits (with an angle close to the impedance angle) but
larger than Vf/Z, șV can go beyond ±90° as a transient, and decrease back since this
point is not a stable operating point. However, for a current reference out of transfer
limits (with an angle deviated from the impedance angle), șV goes beyond ±90° and
continuously moves during LOS event. As will be shown in the next chapter, the
solutions in this thesis will be proposed to modify the current references to stay within
limits close to the impedance angle avoiding large-signal and small-signal instability.
4.5 Conclusion
The LOS – frequency fall/rise has been analyzed in this chapter and shown that the
LOS is occurring when the current reference is out of the current transfer limits
specified in chapter 3. It is shown that the loss of control of vector control and also
deviation from fundamental grid (50Hz) frequency are shown to be main results of
LOS. The reason for the frequency fall/rise during LOS is found to be mainly due to
sustained error in the estimation of the PLL, and integration of the error resulting in
frequency change.
As given in this chapter LOS is resulting in loss of vector control and frequency
deviation. Loss of vector control means that the WT is not able to inject the referenced
95
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
active and reactive current references. As a result, grid code compliance would be
violated. Moreover, if the actual active current becomes high causing active power
injection to the grid without control, the dc link might become discharged during the
fault, if the wind speed is low. Additionally, loss of control of vector control might
create problems during the recovery period of the fault, due to uncontrolled active and
reactive currents.
Deviation from the fundamental grid frequency means phase difference between the
grid voltage and the wind turbine voltage. Such a phase difference can cause adverse
effects to the grid that the grid voltage might be attenuated during the fault. Phase
difference can cause transient problems when the wind turbine is re-synchronizing to
the main grid after the fault. Hence, the LOS has to be avoided.
It is observed that wind turbines’ current injection during severe symmetrical faults is
driving the PLL towards instability. As stated in [79], despite substantial amount of
research on advanced PLL design, instability of PLL in case of weak grid connections
and low voltage faults, and impact of the PLL structure on the WT stability and power
system stability have not been studied sufficiently in literature.
As shown in this chapter, the LOS is occurring due to “inconvenient” current
references, which are out of transfer limits during the fault. An analogy was made to
acceleration of a synchronous generator during a fault due to high input mechanical
power and low output transfer limits. As well-known, for a synchronous generator
without fast acting valves, it is quite difficult to modify the input mechanical power
within the short duration of the fault, to avoid acceleration. However, it is quite
possible for a converter-connected wind turbine to modify the current references within
short duration of the fault, to avoid LOS, which will be basis of the proposed solutions
in the next chapter.
96
Chapter 4 Analysis of Loss of Synchronism during Symmetrical Faults
97
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
Chapter 5
Proposed Solutions for Loss of Synchronism
In this chapter, proposed solutions for Loss of Synchronism (LOS) are given, reviewing
the state-of-the-art solutions in the beginning. First, impact of PLL settings on the
occurrence of LOS is shown and evaluated as a partial solution. Then, limiting the
current injection during severe faults is given as a fundamental reference. Two
methods to prevent LOS while injecting active and reactive currents are proposed;
namely, current injection based on grid X/R characteristics and the novel PLL
frequency based current injection. WPP level implementation issues are also discussed.
A comparison of five injection schemes is provided at the end.
5.1 State-of-the-Art Solutions
Mainly due to distant location of wind resources from central areas, wind power plants
are connected to low short-circuit capacity buses, and also due to continuously
increasing installed capacity of renewable energy sources, more weak grid situations
are encountered. Issues related with weak grid connection of wind power plants and
response of wind turbines during severe faults have been studied thoroughly in the
literature both by academia and industry. Specifically the problems occurring due to
power or current injection during low voltage faults and with high impedance
connection, which resembles the LOS problem given in this thesis, have been handled
only in few studies, which are reviewed below. In [80]-[83], the weak grid problem is
handled mainly for non-faulted grid cases. Only in [56], specifically the stability
problem during low voltage faults is handled.
98
Chapter 5 Proposed Solutions for Loss of Synchronism
Active Current Reduction:
In [56], the problem of instability, which is highly relevant with the LOS studied in this
thesis, is called as “transient stability problem” occurring specifically during low
voltage faults. In accordance with the grid codes, priority is given to reactive current
injection, while active current is injected as the remaining current capacity of the wind
turbine. In [56], active and reactive current transfer limits have been derived, similar to
the limits in this thesis; however the limits derived in [56] and in this thesis are not
consistent with each other completely. In [56], based on the limits derived, it is claimed
that the instability is occurring for high active current injection during very low voltage
faults. An algorithm, called as “voltage dependent active current reduction” is proposed
such that when the voltage is very low during fault, the active current is reduced to
avoid the instability.
Active current reduction action of the proposed algorithm is shown in figure 5.1 as
imposed on the limits derived in this thesis. Two fault cases, where the wind turbine
with 1.25pu current capacity is referenced to inject 1pu reactive current and 0.75pu
active current during faults, are shown. In the case of figure 5.1-(a), the voltage at the
faulted bus is dropping to 20% of the rated, and in figure 5.1-(b) PCC voltage drops to
10%. As seen in figure 5.1-(a), the algorithm is successfully modifying the current
reference from point “a” towards points “b”, “c” or “d”, which are inside the transfer
limits, as a result the instability is avoided successfully. However, for more severe fault
cases as in figure 5.1-(b) (or higher impedance and more resistive connection with
lower X/R ratio), which are not covered within [56], the proposed algorithm cannot
guarantee that current reference to be within the transfer limits. In other words, the
active current can be reduced from point “e” in figure 5.1-(b), towards “g”, which is
within limits but also to “f” or “h”, which are outside transfer limits. Hence the
“voltage dependent active current reduction” algorithm can work for faults, where the
voltage drops to low values such as 20%, and for inductive networks with high X/R
ratio; but can become insufficient for severe faults, where the voltage drops to very low
values (e.g. less than 10%) or highly resistive connection with low X/R ratios.
99
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
I limit =
Vf
Z
Vf
X
I limit =
Vf
Z
Vf
X
Vf
R
I șI
Vf
R
I șI
Fig. 5.1 Active current reduction action for (a) 20% PCC voltage, (b) 10% PCC
voltage.
In [56], instability analysis and transfer limits are accomplished for active and reactive
current injection from wind turbine terminals towards PCC, without specifying the type
of the turbine as DFIG or Full-Converter, since the active reactive current control can
be realized for both. However, impact of instability situation is simulated and assessed
for DFIG, and effects are stated, such as called by “pole-slippage” which is stated to
cause mechanical stress on the machine [56].
Limitation of Power Angle:
In [80], the stability is considered not only for fault cases but also non-fault cases, and
primarily for active power injection. The priority of reactive current injection during
fault is not considered. The instability is proposed to be avoided via limiting the power
injection below the maximum transferrable value, which is calculated online based on
the well-known power-angle characteristic equation.
Pwt =
100
Vwt Vgrid
X
sinșV
(5.1)
Chapter 5 Proposed Solutions for Loss of Synchronism
As well-known, the maximum transferrable power is reached when the phase angle
difference between the wind turbine voltage and the grid voltage, becomes 90°. Such a
situation is shown in figure 5.2, which is in current-angle form, similar to the figure
3.17.
Vgrid constant
Vgrid
ș VVgrid -Z.I
TI
I<Ilimit
ș V =90o
Vwt
TI
-Z.Ilimit
Vwt
I=Ilimit
Fig. 5.2 Power-angle limitation.
In [80], the maximum transferrable power is calculated and active power injection is
reduced in conjunction with the aim of staying within limits. This action is similar to
the “active current reduction” in [56], but for the non-fault case. In [80], the necessary
angle and grid voltage magnitude information is obtained via estimations using voltage
and current measurements at the wind turbine terminals at two instants of time.
Additionally, in order to have higher stability margin, the maximum power transfer
limit is calculated for an angle difference value chosen to be lower than 90°, for
instance 70°. However, this algorithm has the disadvantage that any instability due to
reactive power (current) injection is not considered and the proposed solution is to
cease injection, which would not be acceptable considering grid code requirements.
Current Limitation Based on PLL Estimation Error:
In [81] a method, which is focusing on how to detect a possible instability as quick as
possible, is proposed. It is claimed that in addition to the WT terminal voltage as in
[56] and [80], error of the PLL (Vq voltage signal) have to be used as signals to detect
possible instability. Any significant variation as terminal voltage drop and/or increase
in PLL error, are used as signals for possible instability detection. Similar to [81], the
proposed action to avoid instability is to limit the injection, which is a disadvantage
considering the reactive current injection required by the grid codes.
101
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
Loss of Angle Stability of Weak-Grid-Connected Wind Turbines:
In [82] Loss of (Angle) Stability (LOS) during healthy (non-faulty) conditions is
studied; however, it is stated that instability occurs due to a small disturbance in
healthy conditions or a large disturbance such as a fault. It is stated that when the VSC
is considered as a voltage source, angle instability can occur if the angle difference
between the VSC and grid voltage reaches 90 degrees. The source of instability is
shown to be high grid impedance (mostly reactance is considered), in other words low
SCR connections. The relation of grid strength and the limits for instability is
discussed. A “Voltage Control System (VCS)” is proposed to keep the WT inside the
stable operating points despite the fluctuating wind conditions. In order to avoid
instability a sequence of actions; fast identification of LOS event, stopping the power
feed-in and restoring slowly back (post-LOS control), is proposed. As described above,
reactive current injection during low voltage faults, which is the main scope of this
thesis, is not covered in [82].
In addition to above studies, the instability problem is handled in [83] for VSC and
LCC based HVDC converters, and also for renewable (e.g. wind) power plants are
included in the scope as aggregated single converters. Specifically post-fault instability
due to a change in the grid (line disconnection) is referred to be the source of
instability. Also faulty and healthy (non-faulty) conditions but of a weak grid are
covered. The converters are assumed to be injecting high active power (which would be
valid for a HVDC converter or a WPP during recovery of a fault; but invalid for a WPP
during fault, where primarily reactive current is injected). Instability is referred as
“voltage” and “transmission angle instability” occurring due to exceeding maximum
transferrable power. If the converter continues injecting active power via injecting
active current, the voltage at the output terminals decreases and DC link voltage
decreases, which cause active power to decrease after a level of injection. After that
level, change of active power becomes negative for positive change of active current.
The solution is suggested to measure dP/dt and dI/dt continuously, such that when these
signals have opposite signs, the active power reference is decreased in order to avoid
instability. In this study, LOS during reactive current injection to low voltage faults is
not covered.
102
Chapter 5 Proposed Solutions for Loss of Synchronism
Active Current Control during Grid Faults:
In [84], a new method for active current reference control during grid faults, which is
based on the X/R characteristics of the impedance within WPP and voltage observed at
the PCC bus, is proposed to obtain a current, which is called “optimal”, at the PCC.
The conventional method is described to inject reactive current as required by the grid
codes (e.g. 0.9pu) and also active current (e.g. 0.4pu) in accordance with the power
production of the wind turbine. It is shown that for low voltage faults (Vpcc<20%)
and/or high impedance (especially high reactance) between the wind turbine and PCC,
the injected wind turbine current takes form of reduced (even zero or negative) reactive
component at PCC. This situation is mentioned in remark 3.10 of this thesis to be
originated mainly from reactive (I2X) loss on the impedance, and referring the figure
3.21, the below phasor diagram in figure 5.3 is given to better explain the situation. As
seen in figure 5.3-(a), when highly active current is injected from the wind turbine, due
to low faulted point (PCC) voltage and/or due to high impedance, the PCC voltage
angle deviates from WT; as a result reactive component of current at PCC decreases,
even towards zero such that only active current is supplied to grid for an increased
current magnitude. In figure 5.3-(b), it is seen that for even higher magnitudes of
current, the current starts leading the PCC voltage such that reactive power is absorbed
from the grid (underexcited operation). As also explained above and in chapter 3, this
situation is mainly due to reactive (I2X) loss on the impedance arising due to
excessively high active current injection.
Vwt
Vwt
TI
I Vpcc
TI
Vpcc
I
Fig. 5.3 Decreasing reactive current at PCC with high active current injection from
WT.
103
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
In [84], a method is proposed such that the active current injection from wind turbine is
adjusted (decreased relative to what is injected by conventional method) to a specific
value defined by X/R of the impedance and the PCC voltage as in (5.2) below;
Iactive
Vpcc ·
R§
¨ Ireactive ¸
X©
Z ¹
(5.2)
The action of proposed method is shown as imposed on the current transfer limits
derived in this thesis as in figure 5.4. As seen in figure 5.4-(a), the proposed method is
bringing the highly active current reference of conventional method towards an angle
close to the impedance angle. This method seems similar to the one in [56], except in
[56] active current reference was reduced based on voltage without any specific target
angle, whereas in [84] the active current is adjusted to a specific angle, which can also
work for highly reactive current references. As seen in figure 5.4-(b), with the use of
proposed method, the current with respect to PCC voltage takes a form of high reactive
which is also desired by the grid codes, solving the issue shown in figure 5.3 above.
Vpcc
Vpcc
X
Vpcc
Z
șI
Vwt
Vpcc
R
I
Fig. 5.4 Active current reference control based on X/R and PCC voltage.
In [84], LOS is not considered and results are shown for a moderately severe fault with
10% remaining voltage at PCC. Nevertheless, as mentioned above, the proposed
method brings the current reference close to the impedance angle, which can help to
solve the LOS. However the method in [84] provides highly reactive current at PCC,
which would still cause LOS when a severe fault occurring remote from PCC, as
104
Chapter 5 Proposed Solutions for Loss of Synchronism
mentioned in section 3.3 and shown figure 3.32 in chapter 3. Additionally, as will be
discussed below, for very severe faults (e.g. 2% PCC voltage) the precision
requirement for X/R value estimation becomes very critical that makes the X/R based
methods insufficient to avoid LOS. In [84], the proposed method is tested against X/R
estimation deviances for a fault with 10% PCC voltage, without considering the impact
of severity of the fault on allowed deviances. Additionally, the method in [84] requires
information of PCC voltage during faults, which is stated to be calculated using the
minimum RMS voltage value measured at the wind turbine terminals.
Maximum Voltage Increase with Optimum Current Angle:
In [23], weak (high impedance) and low X/R grid cases are studied both for faulted and
post-fault periods. It is shown that when the current at the PCC of a WPP is injected
with the angle of the impedance of the grid, highest voltage increase at the PCC is
obtained. This situation is represented in figure 5.5 below for a current injection with
constant magnitude and varying angle from WPP. The grid voltage here can be
considered as the voltage at the faulted point, which is a point remote from PCC.
Similarly in first part of [56], similar conclusion has been made, such that during a fault
at PCC, the highest PCC voltage increase can be obtained when the PCC current is
injected with the angle of the grid impedance. However in related part of [56] only a
special case that the fault impedance is having the same angle with the grid impedance
is analyzed. In practical fault impedance can have quite different characteristics than
the grid impedance. Additionally in [8] and [9], impact of active current injection
additional to the reactive current injection during fault is shown to improve the voltage
nearby PCC.
Vpcc
Vgrid
Vpcc
Z=R+jX
șI
Vgrid
Fig. 5.5 Maximum voltage increase at PCC.
105
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
As seen in figure 5.5 and as was also shown in figure 3.19 in chapter 3 of this thesis, at
such an operating point, the sending end (PCC) voltage and receiving end (grid side)
voltage are in phase with each other, which also helps to avoid LOS. Hence such an
injection scheme can help to reduce risk of LOS, however LOS is not considered and
aimed to be solved within these proposed X/R based studies. Moreover, as also
commented above for [84], X/R based methods suffer from precision requirement of
X/R value. In these studies, new methods are proposed based on the X/R of the grid in
order to provide higher voltage boost at wind turbine and PCC terminals, whereas the
wind turbines are assumed to be working properly without any LOS.
Most of the state-of-the-art solutions for weak grid and low voltage fault stability
problems are proposing to limit or cease current injection during fault. In the following
sections of this thesis, novel algorithms are proposed, which can inject currents without
creating instability.
5.2 Impact of PLL Settings to LOS
As given in chapter 4, the source of LOS is “inconvenient” current references which
are out of current transfer limits, and resulting in estimation error within PLL. As
shown in chapter 2 to 4, the LOS in this thesis has been observed as frequency fall,
where the frequency was dropping towards zero, or frequency rise, where the frequency
was increasing towards very high values, due to continuous integration of the sustained
estimation error within PLL. However, the integral action in a practical PLL
application would have saturation and anti-windup algorithms to avoid unnecessary
integration. Taking the PLL structure in figure 5.6 as a reference, saturation limit is
applied to two signals within the PLL; at the integral output and at the calculated
frequency signal. In addition to saturation at the integral output, an anti-windup
algorithm is also implemented. The saturation limit at the output of the integral action
can be chosen as the practical value of steady-state deviation from fundamental
frequency (50Hz), which would be expected or allowed in the grid, where the wind
turbine is connected. Based on generic grid code requirements, which set the allowable
steady-state frequency deviations, the integral output in figure 3 can be limited as +/2Hz, such that the steady-state frequency including the non-faulted conditions would
106
Chapter 5 Proposed Solutions for Loss of Synchronism
vary between 48 and 52 Hz. The saturation value at the calculated frequency cannot be
set with narrow limits around fundamental frequency since the tracking performance of
the PLL would be restricted [44]. In order to allow dynamic changes at the calculated
frequency for better dynamic tracking performance, the saturation limits can be set as
minimum 45Hz and maximum 55Hz. It is important to note that; instead of PI
compensator a PID compensator would be employed, which would be applied with
similar saturation algorithms.
However, as discussed above, the LOS is causing sustained PLL error, due to
“inconvenient” current references. In figure 5.7, a case, where a frequency rise is
observed, is simulated with saturation in PLL applied with maximum frequency limit
of 55Hz. Limiting the integral output or the calculated frequency can prevent
continuous deviation of frequency but cannot prevent sustained PLL estimation error.
Hence, d&q axis estimation is still incorrect during LOS, causing loss of vector control
action. As seen, estimated current components are matching with the referenced, while
the actual current is differing from the referenced.
vq
vd
Fig. 5.6 PLL structure with saturation blocks.
Alternatively, adaptive adjustment of PLL parameters, gains or limits during severe
faults can help to reduce rate of change of frequency during LOS event, since the rate is
highly dependent on PLL dynamics as shown in chapter 4. However, as stated above,
these solutions would not prevent incorrect estimation during LOS. Such a frequency,
thus a phase difference, during fault, might cause resynchronization problems when the
fault is cleared. Hence, adjusting PLL settings cannot be considered as a
comprehensive solution to LOS, which is mainly caused by “inconvenient” current
references. In the following sections, solution based on modifying the active and
reactive current references to avoid “inconvenient” references are given.
107
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
Vwt-a& Iwt-a
(pu)
Iwt Active&Reactive
(pu)
Vpcc-abc&rms
(pu)
Vpcc-a
Vpcc-b
Vpcc-c
1
0
-1
-2
0.9
Vd-pll & Vq-pll
(normalized)
1.1
1.2
1.3
1.4
1.5
1
0.5
0
0.9
1
1.1
1.2
1.3
1.4
1.5
1
1.6
Ireact - ref
Ireact - meas
Ireact - actual
Iact - ref
Iact - meas
Iact - actual
1.6
Vwt-a
Iwt-a
0
-1
0.9
1
1.1
1.2
1.3
1.4
1.5
1
1.6
Vd-pll
Vq-pll
0.5
0
0.9
WT frequency
(Hz)
1
1
1.1
1.2
1.3
1.4
1.5
56
54
52
1.6
WT frequency
50
48
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
time (s)
Fig. 5.7 LOS – frequency rise with saturated PLL.
5.3 Limited Current Injection during Severe Faults
As discussed in section 3.4, current references with magnitude smaller than Vf/Z, which
are shown as the blue circle in the current transfer limits figure 3.33, do not cause LOS
for any injection angle, since that current is always within the transfer limits. The same
as (3.17), the current limit for this case is given in (5.3) again;
Ilimit
Vf
Z
(for 0D <șI <360D )
(5.3)
Before the X/R based and PLL frequency based solutions in the following sections,
limiting the current injection to stay smaller than Vf/Z is given as reference solution
108
Chapter 5 Proposed Solutions for Loss of Synchronism
avoiding LOS. Since for certain grid codes, fault ride-through and reactive current
injection is not required below a specific value (e.g. 15%), limited current injection can
be considered as acceptable, which guarantees stable operation compromising current
injection during fault. However, such a limitation algorithm would also bring practical
implementation issues such that the faulted bus voltage or a remote point (e.g. PCC)
voltage measurement would be required in order to determine the current injection
limit. Therefore, estimation of PCC voltage, or fast communication between the PCC
point and the wind turbines would be required, which might be a challenge considering
the very short duration of the fault. Additionally, as shown in section 3.4 and figure
3.31, the PCC voltage varies with fault location and the transfer limits are varying with
varying fault location. Even though the PCC voltage is known, it is difficult to
differentiate between the fault occurring at PCC and a fault occurring at remote points.
Hence, it is difficult to set the voltage level for limited current injection. As an
example, for the WPP given in figure 2.2, which has impedance of 0.21pu (with X/R of
8) between the wind turbine and the PCC, the safe “injectable” current magnitude
versus remaining voltage at the PCC would be as in figure 5.8-(a) below. Based on the
linear relation in (5.3), the “injectable” current magnitude increases for higher PCC
voltages and 1pu current can be injected when the PCC voltage is larger than the
impedance magnitude (0.21pu in this case). A generic FRT curve is shown in figure
5.8-(b), showing the minimum PCC voltage where 1pu current can be injected.
Fig. 5.8. (a) “Injectable” current magnitude versus PCC voltage magnitude, (b) FRT
curve for 1pu current injection during fault
109
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
As observed in (5.3) and figure 5.8, for WPPs with higher impedance between wind
turbines and the PCC (due to distant location of wind turbines and transformer
impedances) and also with long radial connection lines (underground cables or
overhead lines), the minimum PCC voltage for 1pu “injectable” current would be
higher as expected, for instance as high as 40%.
5.4 X/R Based Active Current Injection
As shown in chapter 3 and 4, LOS is occurring when the current reference is out of the
current transfer limits. The transfer limits, given in figure 5.9, are shown to be based on
remaining voltage at the faulted bus and the impedance between the wind turbine
control terminals and the faulted point. Hence, a straightforward solution against LOS
would be to give active and reactive current references to the wind turbine such that the
referenced current is within the current transfer limits.
I limit =
Vf
Vf
X
Z
șZ
Vf
R
I șI
I limit =
Vf
Zsin( ș Z -ș I )
Fig. 5.9 Current transfer limits.
As seen in current transfer limits, when the current has the same angle of the
impedance, for any magnitude of the current, the operating point is inside the current
transfer limits. The phasor diagram when the current has the same angle of the
impedance angle is shown in figure 5.10.
110
Chapter 5 Proposed Solutions for Loss of Synchronism
Vf
ș I =ș Z
ș V =0o
Z.I wt
Vwt
I wt
Fig. 5.10 Phasor diagram when current angle equal to impedance angle.
The condition that the angle of the current is equal to angle of the impedance implies
that active and reactive currents are related with the X/R ratio of the impedance as
below;
șI =șZ
Ÿ
Iactive R
=
Ireactive X
(5.4)
The grid code requirements are giving priority to reactive current injection during fault,
and active current is allowed to be freely set, for instance to be decreased in order to
stay within the wind turbine current ratings. Hence, for the solutions proposed against
LOS, the reactive current is primarily injected and active current is adjusted by the
LOS solution algorithms as given in the following parts.
The first proposed control algorithm, which is active current injection based on X/R
and the current references are generated based on (5.4), is given in figure 5.11. In figure
5.11, the blocks 1-3 are the same as conventional method, which are employed for nonsevere faults. The core of the solution is given in block-5, where the active current
reference is generated with the ratio of R/X to the reactive current reference. There is
the block-4, decision algorithm, which is enabling either the conventional method
block-3 (for non-severe faults) or the solution block-5 (for severe faults), based on the
enabling from decision algorithm.
The decision algorithm is playing an important role regarding the DC link voltage
regulation for the wind turbine. If the solution is employed for all faults, then the active
current would be set to a specific value during any low voltage fault. However, as
discussed previously, the instability risk exists for severe faults; and for non-severe
111
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
faults active current can be set from the DC link voltage regulator in order to help the
active power flow from machine-side converter. Otherwise, use of chopper resistance
would increase unnecessarily for non-severe faults. Two cases of active reactive current
profiles with and without decision algorithm is shown in figure 5.12 below. It can
easily be concluded that it is better to have the response in figure 5.12-(b), with the
decision algorithm, rather than having the response in figure 5.12-(a), regarding excess
use of chopper resistance. The threshold level to classify a fault whether as severe or
non-severe can be determined based on the installation, i.e. the WPP and grid
characteristics. The block-6 is important in order to keep the current of the WT within
its capacity value. In this block active and reactive current references are down scaled if
magnitude exceeds the capability value.
1
Vfeedback
GridCodeProfile
I*reactive
Igcm
3
ActiveCurrentLimiter
2
V3
VDC
2
I*active
I**
active d IactiveͲlimit
Vfeedback
I**
active
enable
ChopperTrigger
Signal
4
2
*
IactiveͲlimit = Icapable ͲIreactive
V2 V1
DCLinkVoltage
Regulation
I*reactive
DecisionAlgorithm
Vthreshold Vfeedback d V2
useconventional
currentreferences
0 d Vfeedback d Vthreshold
useX/Rbased
currentreferences
6
Imag
enable
I*reactive
5
GridX/RDependent
ActiveCurrent
R
X
I**
reactive
I**
active
CurrentScaling
2
2
**
I**
reactive +Iactive
if (Imag >Icapable )
I***
reactive
I***
active
Icapable
Imag
Icapable
Imag
I***
reactive
u I**
reactive
u I**
active
I***
active
Fig. 5.11. Proposed X/R based current injection algorithm.
As observed in figure 5.12, when the X/R based control method is used, some amount
of active current is injected. For the wind turbines having current capacity larger than
the maximum reactive current requirement of the grid code (i.e. Icapable > Igcm), the active
112
Chapter 5 Proposed Solutions for Loss of Synchronism
current can be given without compromising the reactive current value, as shown in
figure 5.12.
Fig. 5.12. Current references of X/R based solution (a) without, (b) with decision
algorithm.
If the X/R based active current reference is high, such that remaining capacity is not
enough for that amount of active current; or if the wind turbine capacity is not larger
than the grid code reactive current requirement (i.e. Icapable = Igcm), as shown in figure
5.13, then the reactive current injection would be compromised, such that the injected
reactive current magnitude decreases from maximum grid code required amount (Igcm),
to a lower value (Igcm’).
Fig. 5.13 Current references with X/R based solution employing decision algorithm.
The X/R parameter used within the proposed control algorithm is the X/R ratio of the
impedance between the wind turbine control point and the faulted point. However, it is
practically difficult to obtain value of this parameter. It can be commented that the
impedance characteristics of the WPP layout (WT transformers, collector grid, and
WPP transformer) and of a connection line (underground cable/overhead line, if exists)
113
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
can be known from installation data; and the grid characteristics can be obtained from
TSO. Additionally, the X/R parameter can be obtained (or available value’s precision
can be improved) by offline or online estimation methods based on voltage and current
measurements at the wind turbine or WPP level during non-faulty and/or faulted grid
conditions. However, it can be concluded that; despite all the available and estimated
data, the X/R parameter would be obtained with some uncertainty.
.
5.4.1
X/R parameter uncertainty
Due to the X/R parameter uncertainty, the current references would deviate from the
ideal operation of figure 5.10, or even deviate towards out of transfer limits, causing
LOS. As the band of the current transfer limits are becoming narrower for lower fault
voltages (Vf) and/or with increasing impedance magnitude (Z), the risk of deviation out
of transfer limits due to X/R parameter mismatch increases. For very severe faults with
very low faulted point voltage (e.g. 1%), the transfer limits band becomes so narrow
that almost a line and any X/R parameter mismatch cause LOS. In order to calculate the
impedance angle value (tan-1(X/R)) precision requirement, figure 5.14 is utilized. For a
given current magnitude, the allowed uncertainty is calculated based on the current
transfer limits. The current transfer limit equation is solved when the current magnitude
is fixed as in (5.5) to calculate the point where the current reference deviates from
impedance angle reaches the limit line. Assuming that the deviation would be small,
(5.7) is obtained from (5.6).
Vf
Iwt =
Z
sin(șZ șI )
(șZ șI ) | I
șI =șZ B I
114
1pu
Vf
wt
Vf
wt
Z
Z
Ÿ
(in radians)
(in radians)
sin(șZ șI )
Iwt
Vf
Z
(5.5)
(5.6)
(5.7)
Chapter 5 Proposed Solutions for Loss of Synchronism
I limit =
Vf
X
Vf
Z
Vf
R
șZ ș
I
ș I-min
ș I-max
I limit =
Vf
Zsin( ș Z -ș I )
Fig. 5.14 Deviation of current angle from impedance angle.
For instance for a fault with 0.05pu (5%) remaining voltage and impedance magnitude
of 0.3pu between wind turbine and faulted point, the current injection angle cannot be
injected more than ±10° deviation from the impedance angle, in order to stay within the
limits. For a fixed amount of error in the impedance angle estimation, șZ-est-err, a general
rule based on minimum fault (PCC) voltage and impedance magnitude can be obtained
as in (5.8) such that the current reference with estimation error is still inside the transfer
limits;
șZ-est-err d
Iwt
Vf
Z
(in radians)
(5.8)
When the current reference is given with the ±șZ-est-err, as in (5.7), the current would still
be within transfer limits. For instance allowing an estimation error of 10° (0.175
radians) for 1pu current injection; for impedance magnitude of 0.3pu between wind
turbine and faulted point, the minimum remaining voltage has to be above 0.05pu (5%).
Below this value, current reference can go out of transfer limits. Hence, due to
impedance angle estimation uncertainty, the X/R based method can only work for
faults with remaining voltages above a specific value, which is defined by (5.8) based
on estimation precision, impedance magnitude and current injection magnitude.
115
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
In order to save space and since similar cases have been conducted in the previous
parts, simulation or experiment results with X/R dependent active current injection are
not shown. As a reference, the experimental results in figure 4.12 and 4.14 can be
considered as the cases where the X/R based method is not employed and LOS is
observed; and the results in figure 4.13, where the current is injected exactly with the
angle of the impedance is an example for employing X/R based algorithm and
preventing LOS. However, as discussed above, the X/R based algorithm suffers from
the precision requirement for the X/R parameter value.
In summary, the X/R method solves LOS problem for some of problematic cases, but
cannot solve most of the problematic cases due to practical difficulties related to
obtaining and setting the X/R parameter precisely regarding the impedance
characteristics and fault location.
116
Chapter 5 Proposed Solutions for Loss of Synchronism
5.5 PLL Frequency Based Current Injection
In the X/R based current injection method in the previous section, active and reactive
currents were proposed to be injected based on an estimation of X/R of the impedance
between the wind turbines and the faulted point. As mentioned before, such an
injection method, which is kind of open loop forward compensation, easily suffers from
estimation errors. As given in previous parts, a sustained PLL error arises and
frequency deviation occurs when the current reference is out of transfer limits. When a
fixed amount of reactive current is injected in accordance with the grid code
requirements, it is observed that the frequency is falling when active current is low, i.e.
when the current angle is smaller than the impedance angle; and the frequency is rising
when active current is high i.e. when the current angle is larger than the impedance
angle. The PLL frequency based current injection method in this section is based on
this dependency, such that the active current is modified based on the PLL frequency
feedback. As seen in figure 5.15, the active current is referenced by a frequency
regulator algorithm in order to regulate the wind turbine frequency towards prefault
(fundamental) frequency.
I*reactive
*
fwt
50Hz
*
active
I
*
Vout
IabcͲwt
Vabc
VabcͲwt abc Vq
PI
dq
1
s
IabcͲwt
Fig. 5.15 Proposed PLL frequency based active current injection method.
As will be analyzed below, and observed in previous cases, during the LOS event the
frequency is decreasing with less (insufficient) active current and increasing with high
(excess) active current, which is consistent with the classical inertial frequency
behavior in a power system. In fact, as discussed in chapter 3, the current transfer limits
are mainly originating from the issue of conduction power losses on the impedance. For
a fault occurring at PCC or at the main grid connection point, the system becomes like
isolated from the main grid, and power balance between the wind turbine and the
117
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
impedance (between wind turbine and the faulted point) defines the frequency
behavior. It can be considered that the wind turbine isolated (islanded) from the main
grid due to the severe fault and operates as a microgrid. Since the voltage level is very
low due to fault, active power balance can easily be supplied by the wind turbines as
long as there is a minimum amount of generation. It should be noted that in this case of
islanded operation due to fault, there can be no rotational (inertial) element, but only
the wind turbine converter and the line impedance. Hence, the frequency is not the
conventional inertial frequency, which is determined by the mechanical rotation of the
machines; but the electrical frequency which is defined by the PLL.
Dynamic model for the frequency based active current injection method is derived from
the PLL model in chapter 4 figure 4.10, which has been originally developed in [79]. In
the quasi-stationary PLL model, given in figure 5.16, a feedback from the wind turbine
frequency signal is used in the positive feedback path as a corrective term against LOS.
As explained above, a frequency deviation is compensated by acting on the current
reference and decreasing the positive feedback term, Vq+.
v q
vq
v q
Fig. 5.16 Quasi-stationary model of the PLL with frequency compensator [79].
The frequency compensation term, kf, comes in the kș term of the small-signal model as
in (5.9). The frequency compensator is incorporated in the small-signal model and the
transfer function is obtained same as in (4.30), except that the positive feedback term
includes the frequency compensation. Hence, the stability criteria including the
frequency compensation term becomes as in (5.10). Root locus for varying kf gain from
0 to 1 at an operating point with the faulted point voltage, Vf, as 0.05pu and the system
in figure 4.6 is given in figure 5.17 below.
118
Chapter 5 Proposed Solutions for Loss of Synchronism
kș =
RL
Z(Ȧop )
2
kf
(5.9)
Kpcos(șV )Vf > Ki Iwt
2
§
·
Z (Zop )
¨Rk
¸
sin(
ș
(
Z
)
ș
)
L
Z
op
op
f
Z
I
¸
L
Z (Zop ) ¨
©
¹
L
(5.10)
Im(s1,2 )
(Zd )
20
10
Re(s1,2 )
attenuation
(9Zn )
0
-10
-20
-20
-10
0
10
20
Fig. 5.17 Root locus for varying șV, for Vf=0.05pu, for system in figure 4.6.
As seen in figure 5.18, when kf is chosen to be 0.005, a well damped system is
obtained. A root locus for varying șV is given in figure 5.18 employing the frequency
compensator for the system in figure 4.6, when the faulted point (PCC) voltage is
0.05pu. Referring to figure 4.17 in chapter 4, where system closed-loop poles were
driven to right-half plane for șV larger than ±85.3°; it is important to note that the
system closed-loop poles stay in the left-hand plane for any șV value, such that the
frequency compensator is providing small-signal stability when șV moves towards
±90°. As discussed in chapter 4, for șV larger than ±90°, small-signal stability is not
provided though with the frequency compensation since the negative feedback term in
PLL gets negative gain, causing instability.
119
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
Im(s1,2 )
(Zd )
20
10
Re(s1,2 )
attenuation
(9Zn )
0
-10
-20
-20
-10
0
10
20
Fig. 5.18 Root locus for varying șV, for Vf=0.05pu, with Kf=0.005.
The control diagram for the PLL frequency based active current injection method is
shown in Figure 5.19. As discussed above, the reactive current reference is set
primarily based on the grid code requirement and the active current, which is flexible,
is set by the frequency regulation algorithm. The resultant current reference stays
within the transfer limits providing the wind turbine staying synchronized to the grid
frequency. The blocks 1-3 and 6 are performing the same functions described in the
previous X/R based control algorithm. The core of the PLL frequency based control is
given in the block-7. In this block an active current reference, I*active-stab, is generated by
the frequency compensator Kf(s), and this reference is added to the active current
reference generated from the active current limiter function. Therefore, the PLL
frequency based control is like acting in parallel to the conventional method via
modifying the active current reference. The frequency compensator Kf(s) is designed as
a PI compensator to include an integral term for steady-state frequency compensation
during fault. The frequency feedback is obtained by the PLL from the phase voltages
observed at the WT terminals. The calculated frequency is compared with a reference
which can be used as the rated (e.g. 50Hz) or prefault frequency. With the use of
deadband function, which is applied to frequency error, the controller is acting only to
frequency deviations larger than the defined deadband (e.g. +/-100mHz). So, the
120
Chapter 5 Proposed Solutions for Loss of Synchronism
controller does not act unnecessarily for small frequency deviations, which occurs for
non-severe faults (also due to noise in the frequency measurement). Hence, in contrast
to X/R based solution, where a decision algorithm is employed, the PLL frequency
based control has its inherent decision algorithm triggering itself only for severe-faults.
I*reactive
I*reactive
2
2
*
IactiveͲlimit = Icapable ͲIreactive
*
active
I
I**
active d IactiveͲlimit
I**
active
I**
reactive
Imag
2
2
***
I**
reactive +Iactive
I***
reactive
if (Imag >Icapable )
I***
active
I**
active
I*activeͲstab
I***
reactive
I****
active
Icapable
Imag
Icapable
Imag
I**
reactive
I****
active
I***
active
Fig. 5.19 Proposed PLL frequency based control algorithm.
The PLL frequency based control algorithm acts as feedback closed loop system which
substantially improves the response during severe faults, such that the LOS is avoided
for any severe fault, as shown in the following parts with simulation and experimental
results.
5.5.1
Simulation Results of PLL Frequency Based Control
Algorithm
In Figure 5.20, simulation result of the PLL frequency based control method is shown
for a severe fault (from the case in figure 4.2) where pure reactive (zero active) current
is referenced by the conventional method. As seen in second subfigure, the active
current reference Iact-FR from the frequency regulator is generated by the algorithm such
that the frequency (in fifth subfigure) is kept at 50 Hz. As expected the PLL estimation
error (Vq in fourth subfigure) is compensated. In Figure 5.21, the PLL frequency based
121
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
control algorithm is employed for the severe fault (from the case in figure 4.3) where
highly active current is referenced by the conventional method. As seen in second
subfigure, the active current, which is excess and causing frequency rise, is regulated
Vpcc-abc&rms
(pu)
downwards and frequency is kept at 50 Hz.
0
-1
0.9
Iwt Active&Reactive
(pu)
Vpcc-a
Vpcc-b
Vpcc-c
1
1
1.1
1.2
1.3
1.4
1
0
1
1.1
1.2
1.3
1.4
1.5
Vwt-a& Iwt-a
(pu)
0
-1
0.9
1
1.1
1.2
1.3
1.4
1.5
1
Vd-pll & Vq-pll
(normalized)
1.6
Vwt-a
Iwt-a
1
1.6
Vd-pll
Vq-pll
0.5
0
0.9
WT frequency
(Hz)
1.6
Ireact - ref
Ireact - meas
Iact - CM
Iact - FR
Iact - meas
0.5
0.9
1.5
1
1.1
1.2
1.3
1.4
1.5
1.6
WT frequency
55
50
45
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
time (s)
Fig. 5.20 Simulation results with PLL frequency based algorithm – pure reactive case
122
Chapter 5 Proposed Solutions for Loss of Synchronism
Vpcc-abc&rms
(pu)
0
-1
0.9
Iwt Active&Reactive
(pu)
Vpcc-a
Vpcc-b
Vpcc-c
1
1
1.1
1.2
1.3
1.4
1
0
1
1.1
1.2
1.3
1.4
1.5
Vwt-a& Iwt-a
(pu)
1
0
-0.5
-1
1
1.1
1.2
1.3
1.4
1.5
1
Vd-pll & Vq-pll
(normalized)
1.6
Vwt-a
Iwt-a
0.5
0.9
1.6
Vd-pll
Vq-pll
0.5
0
-0.5
0.9
1
1.1
1.2
1.3
1.4
55
WT frequency
(Hz)
1.6
Ireact - ref
Ireact - meas
Iact - CM
Iact - FR
Iact - meas
0.5
0.9
1.5
1.5
1.6
WT frequency
50
45
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
time (s)
Fig. 5.21 Simulation results with PLL frequency based algorithm – highly active case
5.5.2
Experimental Results of PLL-Frequency Based Algorithm
Experimental verification of the PLL frequency based control method is accomplished
with the same setup in figure 4.11. The current reference is given after decreasing the
voltage down to very low (1%) of the rated at t equal to 3.1 second in Figure 5.22.
123
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
During the voltage sag, 1pu reactive current reference is generated as required by the
grid code and the PLL frequency based algorithm generates 0.5pu active current
reference as required by the impedance between WT and PCC terminals, which has
X/R of 2. As seen in third trace, the PLL error signal is kept at zero, and the frequency
1
0
-0.5
2.5
Vd-pll & Vq-pll
(pu)
3
3.5
4
1
4.5
Vwt-a
Iwt-a
0
-1
2.5
3
3.5
4
4.5
Vd-pll
Vq-pll
0.2
0.1
0
2.5
WT frequency
(Hz)
Ireact - ref
Ireact - meas
Iact - ref
Iact - meas
0.5
Vwt-a & Iwt-a
(pu)
Iwt Active&Reactive
(pu)
is regulated towards 50Hz as seen in fourth trace.
3
3.5
4
60
4.5
WT frequency
55
50
45
2.5
3
3.5
time (s)
4
4.5
Fig. 5.22 Experimental results with PLL frequency based algorithm.
In summary, PLL frequency based method is acting as fast frequency control for the
WPP experiencing LOS problem, such that frequency is deviating from the
fundamental frequency of the main grid.
5.6 WPP Level Control
The X/R based and PLL frequency based control algorithms above are implemented at
the wind turbine level. However, usually WTs are operating in parallel in a WPP
structure, with an additional high level WPP level control architecture. When there is a
124
Chapter 5 Proposed Solutions for Loss of Synchronism
WPP controller, which has (voltage and current) feedback from PCC and
communication infrastructure with the wind turbines, advanced schemes at WPP level
can be implemented. Two WPP level control schemes as current control and X/R based
injection at PCC level are discussed below. It should be noted that the PLL frequency
based current injection method does not require any implementation or communication
at WPP level. The WPP level control is only discussed here; any WPP level control
method is not proposed or implemented within this study.
5.6.1
Active and Reactive Current Control at PCC
As seen in chapter 3, during severe faults and/or high WPP internal impedance, the
active and reactive currents injected from wind turbines change their characteristics at
the PCC point, due to phase change of PCC voltage. Referring to remark 3.8 and figure
3.17, when highly reactive currents are injected by wind turbines, current becomes antiphase with PCC voltage i.e. active consumption, as seen in figure 5.23 below. As given
in chapter 1, active current consumption is not allowed during fault by certain grid
codes.
Vpcc
TI
-Z.I
Vwt
I wt
Fig. 5.23 Active and reactive current change from wind turbine to PCC.
Similar case, with highly active current from wind turbine causing reactive power
consumption at PCC, has been studied in [84], as discussed in section 5.1.5 above. As
accomplished in [84], such a situation of active or reactive power consumption at PCC
can be avoided by injecting currents from wind turbines taking this current change into
account, as a forward compensation scheme. In case of a WPP controller at PCC level
and fast communication with wind turbines, active and reactive current control (vector
125
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
control) can be realized at PCC. Implementing such a current control function at PCC,
any active or reactive power consumption during faults at PCC can be sensed and
corrective current references can be sent to wind turbines, as a closed loop feedback
scheme. At the end any active consumption or underexcited reactive current at PCC can
be avoided. However, this would require quite fast communication structure to act in
short duration of the fault. As discussed in chapter 3, with figure 3.32, injection of
controlled current at PCC can help to avoid LOS, especially for faults occurring at
PCC. However, for severe faults occurring remote from PCC, can still cause LOS if
proper current (with the impedance angle) is not injected from PCC. Hence WPP level
current control can help to avoid LOS, but not the ultimate solution.
The X/R based method is based on injection of current from wind turbines with angle
of the impedance. However, when there are additional units installed at the WPP, e.g.
Statcom, energy storage, the supervisory control of WPP controller is definitely
necessary in order to provide parallel operation of WTs and additional units, such that
current is injected with the same angle of the impedance to the grid. Hence, a current
control function as described above can help to coordinate the wind turbines and the
units (e.g. Statcom) at PCC to inject X/R based current at PCC. Moreover, any
triggering or decision algorithm based on grid parameters, can be implemented at WPP
level and necessary triggering commands can be sent to WTs. For instance, the
decision algorithm based on the voltage drop can be employed the WPP controller
based on the voltage drop at the PCC, and necessary commands (triggering either the
conventional method or the proposed method) can be sent to each wind turbine. Such a
grid X/R based current injection at PCC can improve the response regarding avoidance
of LOS; however, as discussed above, the X/R based scheme would still suffer from the
inaccuracy of X/R parameter, especially when there is a severe fault remote from PCC.
5.7 Minimum Active Power Requirement of Proposed
Solutions
Both of the proposed X/R based and PLL frequency based algorithms are based on
certain amount of active current injection during severe faults. However, it is wellknown that active current depends on the active power production level of the WT (or
126
Chapter 5 Proposed Solutions for Loss of Synchronism
WPP). For instance in the cases where PLL frequency based method is employed and
results shown in figures 5.20 and 5.21, 0.25pu active current is injected and the WT
terminal voltage is 0.24pu, which results in injection of 6% of the rated power.
Hence, for some cases, there is the possibility that the WT experiences a severe fault,
but the required active power related to the required active current by the proposed
algorithms, is larger than the available active power at that moment. In this case, if the
WT tries to inject the active current, it can cause drop of DC link voltage, which should
be avoided. The most straightforward way to consider this minimum active power
requirement is to add a function to check for the available active power and limit the
active current reference from stability algorithms based on this limit. It should be noted
that while limiting the active current due to lack of necessary active power, the reactive
current injection needs to be limited in order to avoid instability. This implies that
when the wind power plants are generating very low or zero active power due to low
wind, they should not be expected to inject reactive current during severe faults, since
they would not be able inject the necessary accompanying active current.
5.8 Summary of the Current Injection Schemes
In figure 5.24 five current injection schemes given in this thesis avoiding LOS are
summarized with their (reactive) current injection and corresponding FRT profiles. The
conventional method from chapter 1 is not included here since LOS is not avoided and
occurs with conventional method when the current reference is out of the transfer
limits. First three schemes in figure 5.24 are based on limiting the current injection
during severe faults, considering the current transfer limits. The fourth one is the X/R
based injection method and the last one is the PLL frequency based injection method. Z
in figure 5.24 is the magnitude of the impedance between wind turbine and PCC,
whereas R is the resistance of this impedance.
The first method, keeping the current reference as zero during severe faults is given as
a reference. As seen in (a), current is kept as zero when the PCC voltage magnitude is
below the magnitude of Z based on (5.3), such that no risk of LOS remains. In this
case, the current can be considered as reactive but any current from wind turbine is kept
as zero. The corresponding voltage FRT profile is shown in (b). It is important to note
127
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
that such a scheme is the safest and simplest one avoiding LOS. However, it has the
drawback that no current is injected below a voltage level (e.g. 21% for the system in
figure 4.6), which would not be acceptable for certain grid codes’ FRT requirements.
The second method in (c) is the limited current injection given in section 5.3. The
current magnitude (composed of active and reactive components) is gradually
decreased in order to stay inside the safe transfer limits for decreasing magnitude of
PCC voltage based on (5.3). In this case, again current magnitude is compromised from
maximum value, and the FRT curve in (d) would not comply with certain grid code
requirements.
The third method in (e) and (f) is based on pure reactive current injection, without any
active current. As analyzed in chapter 3, the minimum PCC voltage magnitude in this
case is equal to R of the impedance, as seen in (e) and (f). Remembering the discussion
in section 5.6.1 and remark 3.8, active current is absorbed (active power consumed) at
the PCC, which would not be accepted by certain grid codes.
In the first three schemes, current injection is being limited based on the voltage at the
PCC and impedance between PCC and wind turbine. However, since the current
transfer limits vary with varying fault location, there is the difficulty of sensing the
faulted point voltage and limiting the current accordingly. As shown in figure 3.31,
PCC voltage varies depending on the fault location. Nevertheless, these methods help
to avoid LOS, but compromising current injection. Hence, limiting current injection is
not a comprehensive solution.
In the fourth scheme, current is injected based on X/R of the impedance. As discussed
in section 5.4.1, due to sensitivity to X/R parameter, this method cannot work
satisfactorily for very severe faults. Assuming that the impedance will be estimated
with ±10° accuracy, the minimum voltage for satisfactory performance of the X/R
based method is found as 0.15x|Z|, based on (5.8). In figure 5.24, the current is kept as
zero below this minimum voltage value. The fifth method, PLL frequency based
current injection can inject full current even for zero PCC voltage as given in (i). As
seen in (j) the FRT curve with the PLL frequency based injection method complies
with any grid code requirement. In summary, during severe three-phase grid faults,
LOS problem is occurring due to PLL instability with high current injection from wind
128
Chapter 5 Proposed Solutions for Loss of Synchronism
turbines. The proposed PLL frequency feedback based current injection method is the
strongest candidate to solve the LOS problem during low voltage faults.
The X/R based methods and the proposed PLL frequency based methods are injecting
active and reactive currents to the faulted grid in proportion to the characteristic of the
grid impedance during fault. Such an injection is similar to the active and reactive
power injection of CPPs, which behave as constant voltage sources during faults and
inject power in proportion to the grid impedance during fault [1]. Hence, it can be
commented that the proposed methods are resulting in WPP behavior in a similar
manner to CPPs.
129
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
Fig. 5.24 Comparison of current injection schemes during fault.
130
Chapter 5 Proposed Solutions for Loss of Synchronism
131
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
Chapter 6
Analysis of Asymmetrical Faults
In this chapter, the identified problems during asymmetrical grid faults, which were
given in chapter 2, are analyzed in detail. First, effects of unbalanced grid voltages on
the power system are summarized as a background for asymmetrical fault solutions.
Equivalent circuits of positive negative and zero sequence networks during
asymmetrical faults, which are well-known from classical power system theory, are
utilized to explain the impact of wind power plant current injection on the grid, and the
problem of high phase overvoltages and higher negative sequence voltages.
6.1 Effects of Unbalance
In chapter two, where the identified problems during asymmetrical faults were given, it
has been shown that with the use of conventional method of current injection, higher
negative sequence voltages and higher phase overvoltages are observed. Before the
analysis of these problems and solutions via reducing negative sequence voltage in the
following parts, effect of negative sequence voltage, i.e. unbalance in the grid, is
reviewed in this section. A survey of literature [88] – [101], which studies long-term
(steady-state) and short-term (asymmetrical fault related) effects of unbalance on the
power system elements and stability is accomplished in following paragraphs.
Effects of unbalance on electrical equipments differ from equipment to another.
Common problems due to unbalance are given below for various components in the
power system. Effects of unbalance on rotating machines, induction machines and
synchronous generators, are widely analyzed in literature. Induction machines face
three kinds of problems due to unbalance [88], [89]. First, the machine cannot produce
132
Chapter 6 Analysis of Asymmetrical Faults
its full torque as the negatively rotating magnetic field of the negative-sequence causes
a negative braking torque that has to be subtracted from the base torque linked to the
normal rotating magnetic field. Secondly, the bearings may suffer mechanical damage
because of induced torque components at double system frequency. Thirdly, the stator
and, especially, the rotor are heated excessively, possibly leading to faster thermal
aging. Synchronous generators exhibit phenomena similar to those described for
induction machines, but mainly suffer from excess heating. Special care must be
devoted to the design of stabilizing damper windings on the rotor, where the currents
are induced by the negative and zero sequence components [88], [89].
Unbalance has also effect on capacity of transformers, cables and lines. The capacity of
transformers, cables and lines is reduced due to negative sequence components. Any
circulating current in the delta side of a transformer causes heating and the associated
zero sequence magnetic flux passes through constructional parts of the transformer
causing parasitic losses in parts such as the tank, sometimes requiring an additional
derating [88], [89]. Power electronic converters, which are present in many devices
such as adjustable speed drives, PC power supplies, efficient lighting, can be faced with
additional, uncharacteristic, harmonics. The design of passive filter banks dealing with
these harmonics must take this phenomenon into account [88], [89].
For renewable generating units with asynchronous generators; in its normal slip range
an asynchronous generator has almost constant negative sequence impedance. High
current unbalance can have detrimental effects on the rotor vibration, causing
oscillating torque that increases fatigue in the mechanical drive train of the turbine,
which may alert the mechanical protection system. So at low wind speeds unbalanced
operation can lead to generator disconnection and increased mechanical stresses [92].
From power system transient stability point of view, specifically short-term unbalance
during asymmetrical faults is investigated in literature. In [94]-[96], transient stability
analysis for synchronous and asynchronous machines is extended to include the
unbalanced cases, such as unbalanced load, lines and an asymmetrical fault. An
important finding of the investigation in [94] is in networks equipped with single-pole
circuit breakers, the SLG fault followed by a line outage represents a worse shock to
the system than the traditionally accepted temporary three-phase-to-ground fault. In
133
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
[99]–[101], requirements for allowable negative sequence current flow into rotational
machines are specified as I2t values.
In summary, regarding the stability of the synchronous and asynchronous machines
during asymmetrical faults, only the series asymmetrical faults can be considered as a
risk, not the shunt asymmetrical faults. Any unbalance, which exists for steady-state in
the system, can cause long-term detrimental effects on the components. Hence, steadystate unbalance has to be mitigated by means of hardware and software schemes, and
has to be taken into account within design of power system. When the unbalance is
caused by an asymmetrical fault, the same detrimental effects exist for a very shortterm but with high order of severity. Every occurrence of an asymmetrical fault, adds to
the fatigue in the mechanical and electrical part of power system elements. Hence,
unbalance, i.e. negative sequence voltage, should be mitigated as much as possible
during the faults.
6.2 Analysis of the Problems Observed
As given in chapter one, in most of the grid codes of certain countries, WTs are
expected to stay connected and to support the positive sequence grid voltage with
positive sequence reactive currents during short-circuit grid faults, for both
symmetrical and asymmetrical faults [14]. However, grid codes are prepared to target
only positive sequence voltage boost, which can be considered as a proportional
voltage control in positive sequence.
As known from power system fault analysis [3], during asymmetrical faults, phase-toground voltages in non-faulty phases rises over rated values, i.e. phase overvoltages
occur. Neutral grounding of the power system is designed to keep zero sequence
impedances in accordance with the target of avoiding high phase overvoltages but also
avoiding very high fault currents during asymmetrical faults. For instance, a bus is
considered to be effectively grounded if the ratio of zero sequence impedance to
positive sequence impedance seen from that bus is kept between one and three [3]. This
practice in transmission system keeps the earth fault factor, which is per unit value of
non-faulty phase voltage value, e.g. less than 1.4, which in turn means avoidance of
134
Chapter 6 Analysis of Asymmetrical Faults
phase overvoltages. It should be noted that impedance grounding can be applied in
distribution systems.
An interesting phenomenon, which was presented in chapter two, that; in case of
asymmetrical faults, if the conventional method (CM) is employed, which is injection
of pure positive sequence currents and keeping negative sequence currents as zero,
positive sequence voltage is boosted, but also negative and zero sequence voltages are
boosted at the fault point (e.g. PCC). In the following section, the reasons of coupling
between positive negative and zero sequence voltages during asymmetrical faults, and
impact of WPP current injection is analyzed.
6.2.1
Coupling Phenomenon during Asymmetrical Faults
As well-known from power system fault analysis, positive, negative and zero
sequences are interconnected at the faulted point through the fault impedance [3], [24].
Hence, sequence voltages are coupled at the faulted bus. Due to this coupling, an action
in one of the sequences has effects also on the other sequences. Amount of coupled
boost in negative and zero sequences depends primarily on how much the voltage at the
faulted point can be altered by the WPP, and also depends on the fault type and fault
impedance. Transfer impedance between the WPP and the faulted point defines how
much the WPP can alter the voltage at the faulted bus [24]; and the transfer impedance
depends on the grid characteristics and fault location. For weak grids (with high grid
impedance) and/or for faults occurring near to WPP, coupling is more observed, since
WPP can alter the bus voltage more for weak grids, than for a strong grid [32].
Coupling can be better understood when sequence voltages at the faulted point is
compared for two cases as; with and without current injection from WPP during the
fault. Interconnected equivalent sequence circuits are utilized to show effect of
coupling; as for a SLG fault in figure 6.1 [34], [3], [24]. Impact of positive sequence
voltage boost obtained by the WPP current injection is superimposed to the positive
sequence equivalent voltage, and resulting impact on the negative and zero sequences
are simply calculated via voltage division. The equivalent voltage source V+th is the
prefault voltage at the faulted point, which depends on the power flow before the fault
and usually kept at rated (1pu) value via voltage control action of power plants [34],
135
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
[3], [24]. However, positive sequence reactive current injection by WPPs during the
fault can be considered as additional reactive power support which was not being given
before the fault, and which boosts all phase voltages. Boost obtained by the WPP
current injection on the faulted point positive sequence voltage, V+¨wpp, can be
calculated as (6.1) by using the positive sequence transfer impedance Z+fw, from the
WPP current injection bus to the faulted point and the WPP current phasor I+w.
+
V'wpp =Zfw
Iw
(6.1)
Positive, negative and zero sequence voltages for a SLG fault and effect of WPP
support are obtained as in (6.2) to (6.4), from figure 6.1. It is important to note that the
voltage boost by WPP, V+¨wpp, and the impedance Z+ff, Z-ff and Z0ff, are complex
quantities. Based on the equations derived below, approximate calculations can be done
for sequence voltages, which is used for understanding of coupling action. Detailed and
precise analysis requires time-domain simulations, which is given in the following
chapter.
§ Z - Z 0 +3Z
·
+
+
Vf-SLG
=(Vth+ +I +w Z fw
) ¨ ff - ff 0 f ¸
© Z ff +Z ff Z ff +3Z f ¹
§ Z - Z 0 +3Z
·
(Vth+ +V'+wpp ) ¨ ff - ff 0 f ¸ (6.2)
© Z ff +Z ff Z ff +3Z f ¹
§
·
Z -ff
+
Vf-SLG
=(Vth+ +I +w Z fw
)¨ ¸
0
© Z ff +Z ff Z ff +3Z f ¹
§
·
Z ff(Vth+ +V'+wpp ) ¨ ¸ (6.3)
0
© Z ff +Z ff Z ff +3Z f ¹
0
Vf-SLG
§
·
Z 0ff
+
(Vth+ +I +w Z fw
)¨ ¸
0
© Z ff +Z ff Z ff +3Z f ¹
§
·
Z ff0
(Vth+ +V'+wpp ) ¨ ¸ (6.4)
0
© Z ff +Z ff Z ff +3Z f ¹
V'+wpp
+
I +w Zfw
+
th
V
Zff+
I0fault
Ifault
+
Ifault
Z0ff
Zff
+
Vf-SLG
Vf-SLG
3Zfault
Fig. 6.1. Equivalent circuits during SLG fault.
136
0
Vf-SLG
Chapter 6 Analysis of Asymmetrical Faults
As observed in figure 6.1 and in (6.2) to (6.4), for a SLG fault, amount of positive
sequence voltage boost obtained by WPP current injection, is reflected to negative and
zero sequence voltages inevitably, with ratios depending on sequence impedances. For
instance, for a system with magnitude of Zfw 0.2pu, injection of 1pu WPP positive
sequence reactive current can boost positive sequence voltage approximately by 0.15pu
based on (6.2). However, due to the coupling as observed in (6.3) and (6.4), negative
and zero sequence voltages are also boosted approximately by 0.05pu and 0.1pu,
respectively.
Positive, negative, and zero sequence equivalent circuits seen from the faulted bus
during a DLG fault are interconnected as shown in figure 6.2 [34], [3], [24]. From
figure 6.2, positive, negative and zero sequence voltages for a DLG fault and effect of
WPP support can be obtained as in (6.5) to (6.7).
§ Z - //(Z 0 +3Z ) ·
+
+
Vf-DLG
=(Vth+ +I +w Z fw
) ¨ ff - ff 0 f
¸
© Z ff +Z ff //(Z ff +3Z f ) ¹
§ Z- //(Z 0 +3Z ) ·
+
Vf-DLG
=(Vth+ +I +w Zfw
) ¨ ff - ff 0 f
¸
© Z ff +Zff //(Z ff +3Z f ) ¹
0
Vf-DLG
§ Z 0ff
· ¨ 0
¸ Vf-DLG
© Z ff +3Z f ¹
§
·
Z 0 +3Z
(Vth+ +V'+wpp ) ¨ - ff 0 f
¸
Z
2Z
+6Z
© ff
ff
f ¹
§
·
Z 0 +3Z
(Vth+ +V'+wpp ) ¨ - ff 0 f
¸
Z
2Z
+6Z
ff
f ¹
© ff
§
·
Z 0ff
(Vth+ +V'+wpp ) ¨ ¸ Vf-DLG
0
© Z ff 2Z ff +6Z f ¹
(6.5)
(6.6)
Vf-DLG
(6.7)
As observed in figure 6.2 and in (6.5) to (6.7), for a DLG fault, the positive and
negative sequence voltages at the faulted point are equal. When the fault impedance
(e.g. 0.02pu), which is small compared to positive sequence impedance (e.g. 0.2pu), is
neglected, zero sequence voltage is also equal to the positive sequence voltage, thus the
zero sequence voltage is also boosted at the faulted point (e.g. PCC) with almost the
same amount. Hence, if the positive sequence voltage is boosted by the WPP at the
faulted point (e.g. PCC), the negative sequence voltage is also inevitably boosted to the
same value due to coupling. For instance, for a system with magnitude of Zfw 0.2pu,
137
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
injection of 1pu WPP positive sequence reactive current would boost positive sequence
voltage approximately by 0.1pu based on (6.5), but also the negative and zero sequence
voltages with the same amount as seen in (6.6) and (6.7).
V'+wpp
+
I +w Zfw
Vth+
Zff+
I0fault
Ifault
+
Ifault
Z0ff
Zff
+
Vf-DLG
0
Vf-DLG
Vf-DLG
3Zfault
Fig. 6.2 Equivalent circuits during DLG fault.
Positive and negative sequence equivalent circuits seen from the faulted bus during a
LL fault are interconnected as shown in figure 6.3 below. As well-known, zero
sequence remains unaffected and zero sequence voltage does not arise during LL faults
[34], [3], [24]. From figure 6.3, positive, negative and zero sequence voltages for a LL
fault and effect of WPP support can be obtained as in (6.8) to (6.10).
§ Z- Z
·
+
+
Vf-LL
=(Vth+ +I +w Z fw
) ¨ ff - f ¸
© Z ff +Z ff Z f ¹
§ Z- Z
·
(Vth+ +V'+wpp ) ¨ ff - f ¸
© Z ff +Z ff Z f ¹
(6.8)
§
·
Z -ff
+
Vf-LL
=(Vth+ +I +w Zfw
)¨ ¸
© Z ff +Z ff Zf ¹
§
·
Z ff
(Vth+ +V'+wpp ) ¨ ¸ Vf-LL
© Zff +Z ff Z f ¹
(6.9)
0
Vf-LL
0
(6.10)
As seen in figure 6.3, and also in (6.8) and (6.9), positive and negative sequence
voltages are almost equal at the faulted bus (e.g. PCC) for LL faults, which means that
the boost of positive sequence voltage would be observed with same amount in
negative sequence voltage. For instance, for a system with magnitude of Zfw 0.2pu,
injection of 1pu WPP positive sequence reactive current would boost positive sequence
138
Chapter 6 Analysis of Asymmetrical Faults
voltage by 0.1pu, but also the negative sequence voltage approximately with the same
amount as 0.1pu based on (6.8) and (6.9). Utilizing (6.2) to (6.9), effect of WPP
injection at the faulted bus is obtained approximately. In order to obtain exact voltage
values during fault, and to see effect of WPP injection and also prefault operation,
time-domain simulations are needed, as given in next chapter.
Ifault
+
Ifault
V'+wpp
+
I +w Zfw
Zff+
+
th
V
Zff
+
Vf-LL
Vf-LL
Zfault
Fig. 6.3 Equivalent circuits during LL fault.
The coupling explored in this section has not been observed in previous wind power
asymmetrical fault studies. This is due to the fact that in the previous studies
asymmetrical faults was not created as realistic events as short-circuits (solid or with a
fault impedance) between phases and/or ground; instead unbalance was being created
via modifying voltage sources, which represent grid voltage in the simulation models.
Hence, in previous studies, interconnection of positive negative and zero sequences did
not exist and it was being observed that when the positive sequence voltage is boosted
via injecting pure positive sequence currents, negative sequence voltage remains
unaffected. However, as shown here, sequences are coupled and it is important to
conduct real faults for asymmetrical fault studies in order to observe interconnection
between sequences, especially for high wind power penetration cases.
It is important to note from figures 6.1 to 6.3 that coupling also exists from negative
sequence to positive and zero sequences, such that when negative sequence voltage is
attenuated by WPPs, positive sequence voltage is also attenuated due to coupling.
139
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
Hence at the faulted bus it becomes as a trade-off between boosting positive sequence
voltage and balancing the phase voltages.
6.3 Conclusion
In this chapter, the problems observed with the conventional method of injecting pure
positive sequence reactive current to asymmetrical faults, are analyzed. The coupling
phenomenon, which has not been considered in the previous wind power fault studies,
is explored, together with the impact of WPP reactive current injection. As discussed in
this chapter, negative sequence voltage has numerous harmful effects on the power
system elements, which implies need for attenuation of negative sequence voltage.
In this chapter and chapter two, it is shown that the conventional method of injecting
pure positive sequence reactive current has beneficial effects (boosting the positive
sequence voltage) but also adverse effects (boosting negative sequence voltage and
non-faulty phases). In the next chapter, an alternative to conventional method, dualsequence (DS) control method is given.
140
Chapter 6 Analysis of Asymmetrical Faults
141
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
Chapter 7
Control Solutions for Asymmetrical Faults
In this chapter, based on the analysis of the problems during asymmetrical grid fault
from previous chapter, a control solution to mitigate the mentioned problems is given
as an alternative to the conventional method. A cost function is defined for grid voltage
improvements, which helps to quantify and compare conventional and alternative
control solutions. It is shown that, behaving in a similar manner to the conventional
power plants, response of wind power plants can be improved for better grid support.
7.1 Dual-Sequence Current Injection Method
The response of WPPs during asymmetrical faults have been studied in the literature
[58]-[73], and several control methods injecting negative sequence current have been
proposed; e.g. to mitigate power and dc link oscillations from the WT, or to balance the
grid voltage by reducing the negative sequence voltage. However, these methods
mainly targets issues related to WTs themselves or include negative sequence voltage
attenuation but not handling the situation considering grid side impact of the WPP
current injection during asymmetrical faults. Only in [73], overvoltages at the nonfaulty phases are discussed. However, the coupling phenomenon between positive,
negative and zero sequences, which causes undesired boost of negative sequence
voltage has not been considered in any of the previous studies.
Impact of WPP’s pure positive sequence current injection during asymmetrical faults is
given in the previous sections. It is shown that, a WPP, employing CM, is causing high
negative sequence voltage and high phase overvoltages since WPP is acting as open
circuit in negative sequence. Alternative to the CM, which is injecting pure positive
sequence reactive (capacitive/overexcited) currents by WPPs, the concept of dual
142
Chapter 7 Control Solutions for Asymmetrical Faults
sequence (DS) injection is represented here. DS is based on injecting both positive
sequence reactive (capacitive/overexcited) currents boosting the positive sequence
voltage and negative sequence reactive (inductive/underexcited) currents reducing the
negative sequence voltage, as given in figure 7.1.
In contrast to the grid code requirement, where all phases, hence including the nonfaulty phases are supported, the DS method distributes the support such that only
faulted phases are supported, and non-faulty phases are not supported unnecessarily.
Hence, high phase overvoltages in the non-faulty phases are mitigated, and support is
shared as between positive sequence voltage boost and negative sequence voltage
reduction. The DS method is shown in figure 7.1, where the main contribution of DS
method is the negative sequence voltage control in parallel to positive sequence voltage
control. Hence in DS method, there is also negative sequence proportional voltage
control gain k-, in addition to the positive sequence proportional voltage control gain,
k+, which was shown in conventional control method in chapter one. These parameters
can simply be tuned as having identical values, as is done in this study, whereas
alternative tuning methods can be accomplished for setting different priorities between
boosting positive and reducing negative sequence voltages.
+
Vref
k
Vwt+
+*
Ireactive
+*
Iactive
*
TABC
*
Ireactive
Vwt
k
Fig. 7.1 Dual-Sequence (DS) current injection method.
143
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
Performance of the DS method is shown in the next section with simulations, where
two other methods are also included for comparison.
7.2 Simulation Results
The performance of the proposed DS method, which is injecting both positive and
negative sequence currents, is compared against the CM in this section. In order to see
the bus voltages during faults without support of the WPP, a third injection case of no
support (NS), where WPP is keeping its currents as zero, is also implemented. Three
injection methods, namely NS, CM, and DS are simulated. The system used in the
simulations, and its equivalent circuits for each sequence are shown in figure 7.2 and
figure 7.3, respectively. The negative sequence network is the same as the positive
sequence network with zero grid voltage [24]. The grid is modelled with its Thevenin
equivalent and the WPP is connected to the grid via 50km long OHL. The OHL and
collector network equivalent are modelled as PI models, with details in table 7.1. In the
WPP a d5YN and YNd5 type transformers are utilized as WPP main transformer and
WT transformer, respectively. The collector network’s neutral is grounded via a
grounding zigzag transformer.
Z filter
fault
Fig. 7.2. WPP connection, Thevenin equivalent of grid, and fault location.
Vgrid
fault
fault
Fig. 7.3. Networks of (a) positive and negative sequences, (b) zero sequence
144
Chapter 7 Control Solutions for Asymmetrical Faults
Table 7.1
Electrical Data of Lines and WPP Components, Sbase=100MVA, [pu]
R
X
B
Pos.
0.01
0.1
-
Neg.
0.01
0.1
-
Zero.
0.02
0.2
-
Pos.
0.022
0.112
0.026
Neg.
0.022
0.112
0.026
Zero.
0.088
0.372
0.014
Equivalent
Pos.
0.0056
0.0069
0.0175
Collector
Neg.
0.0056
0.0069
0.0175
Network
Zero.
0.0589
0.0039
0.035
Main Trf
0.01
0.15
-
WT Trf
0.008
0.08
-
ZZ Trf
0.01
0.1
-
WT filter
0.01
0.1
0.05
Fault Impedance
0.02
0
0
Grid
OHL
In the WT, deadband in the voltage control algorithms are kept as zero, i.e. not applied.
Proportional voltage control constant, k+, for the CM case is selected as 5, and the two
proportional constants, k+ and k- for DS (control structure given in figure 7.1) case are
both kept identical as 2.5. The maximum current that can be injected by the WPP is
kept as 1pu. The WPP currents and voltages are measured at the WT terminals. In
order to show impact of WPP reactive current injection on grid voltages clearly, only
reactive currents are injected during the fault and active current is kept as zero.
Time-domain response for a single line-to-ground fault is shown in figure 7.4, where
the fault is created at phase “a”. In order to save space, all three control algorithms are
executed during the fault, keeping the fault duration intentionally long as 300ms. Fault
is created at t=1.1 second, which is removed at t=1.4. Before and after the fault, the
WPP is injecting 20% active power, and 0.2pu balanced phase currents are seen in
figure 7.4-(a). For the first 100ms of the fault, WPP currents are kept zero, i.e. NS is
applied, in order to observe the case without the WPP support. The rms current values
145
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
shown in figure 7.4-(b) are pure reactive components for both positive and negative
sequences. At t=1.2, CM is activated and pure positive sequence currents are injected
as a positive sequence proportional voltage control. At t=1.3, the DS method is
activated and both positive and negative sequence voltage control are realized via
injecting both positive and negative sequence currents. In the figure 7.4 Vf represents
the voltage at the faulted point.
It is important to note that even though the zero sequence networks of grid and WPP
are isolated with the use of dYN transformer, the zero sequence voltage is still
increased with use of CM, when compared to NS due to coupling between sequences. It
rises inevitably also for DS, but nevertheless negative sequence voltage is attenuated
with DS, providing balanced voltages.
It is seen in figure 7.4-(c), at the faulted bus the healthy phase voltages, which are
1.08pu without WPP support, rise up to 1.13pu, when CM is employed. Similarly at
PCC in figure 7.4-(e), healthy phases rise up from 0.95pu to 1.04pu value when CM is
employed, as shown in figure 7.4-(e). With the use of DS method, at the PCC bus
positive sequence voltage is boosted to 0.78pu, negative sequence voltage is attenuated
to 0.23pu, and phase overvoltage is mitigated.
1
0
-1
1
0.5
0
I+WPPͲreactive
IWPPͲreactive
2
0
-2
1
VF+
0.5 VF
0
VF0
2
0
-2
1
+
Vpcc
0.5 Vpcc
0
Vpcc
0
1.05
1.1
1.15
1.2
Fig. 7.4. Simulation results for a SLG fault
146
1.25
1.3
1.35
1.4
1.45
Chapter 7 Control Solutions for Asymmetrical Faults
Since the focus is only on the steady-state period of the faulted duration for DLG and
LL faults, time-domain results are given in tables 7.2 and 7.3, showing values for
steady-state period of each algorithm. Results of DLG fault is summarized in table 7.2,
which shows similar behaviour of SLG fault. As observed in table 7.2, at the faulted
bus with CM, all the phase voltages are boosted, which means that the non-faulty phase
“a” is boosted unnecessarily from 1.11pu to 1.21pu, where the positive sequence
voltage, but also the negative sequence voltage due to the coupling, are both boosted
from 0.39pu to 0.43pu. Hence high overvoltages are observed at the faulted bus and the
PCC bus. At the PCC bus, DS method is boosting the positive sequence voltage from
0.39pu to 0.47pu while attenuating the negative sequence voltage from 0.39pu to
0.35pu, avoiding unnecessary support to non-faulty phase via boosting only the faulted
buses, “b” and “c”, whereas non-faulty phase “a” is slightly boosted from 0.87pu to
0.91pu. It should be noted that DS method is boosting and balancing at the PCC
compromising high boost obtained by CM, which is from 0.39pu to 0.54pu.
Results for a LL fault are given in table 7.3, where it is seen that with the use of CM
both the positive and negative sequence voltages are boosted with the same amount of
0.03pu at the faulted bus due to the coupling, where the non-faulty phase “a” is boosted
unnecessarily from 1pu to 1.06pu; and at the PCC bus the non-faulty phase “a” is
boosted from 1.01pu to 1.12pu. Due to the coupling between positive and negative
sequences at the faulted bus DS method is compromising boost of positive sequence
voltage while avoiding the boost of the negative sequence voltage. However, with the
balancing effect of the DS method, at the PCC bus positive sequence voltage is boosted
and negative sequence voltage is attenuated such that the support is distributed and
only faulted phases are boosted.
As seen from figure 7.4 and table 7.2and 7.3, with the use of DS method, peak values
of WT phase currents are decreased, which can give chance to additional utilization of
the WT for more currents to inject more reactive or active power during the fault.
147
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
Table 7.2
Simulation Results for a DLG Fault
Iwt
Vf
Vpcc
NS
CM
DS
Pos.
0
1.00
0.60
Neg.
0
0
-0.40
a
0
1.00
0.21
b
0
1.00
0.85
c
0
1.00
0.89
Pos.
0.39
0.43
0.40
Neg.
0.39
0.43
0.40
Zero
0.35
0.38
0.35
a
1.11
1.21
1.13
b
0.14
0.16
0.14
c
0.14
0.16
0.14
Pos.
0.39
0.54
0.47
Neg.
0.39
0.43
0.35
Zero
0.10
0.11
0.10
a
0.87
1.06
0.91
b
0.31
0.42
0.35
c
0.31
0.40
0.34
In summary, when only positive sequence reactive current is injected in the case of
CM, non-faulty phases are also boosted unnecessarily, which causes severe increase in
the phase-to-ground voltages of non-faulty phases. DS method is able to avoid adverse
effects of CM such that coupling is mitigated, negative sequence voltage is attenuated
towards WPP, and high phase overvoltages are mitigated. As a drawback of DS method
the grid voltages are balanced for the expense of less amount of boost positive
sequence voltage.
148
Chapter 7 Control Solutions for Asymmetrical Faults
Table 7.3
Simulation Results for a LL Fault
Iwt
Vf
Vpcc
NS
CM
DS
Pos.
0
0.53
0.49
Neg.
0
0.0
-0.51
a
0
0.53
0.12
b
0
0.53
0.80
c
0
0.53
0.92
Pos.
0.51
0.54
0.51
Neg.
0.49
0.52
0.49
Zero
0.00
0.00
0.00
a
1.00
1.06
1.00
b
0.59
0.62
0.59
c
0.42
0.44
0.41
Pos.
0.51
0.60
0.57
Neg.
0.50
0.52
0.44
Zero
0.00
0.00
0.00
a
1.01
1.12
0.91
b
0.59
0.67
0.62
c
0.42
0.46
0.41
A comparison of the calculated cost for each case is given in figure 7.5 below. Cost is
calculated at the grid side as; Cost=|¨Vpos|+|Vneg|+|max (Va, Vb, Vc)-1| (if any phase
exceeds 1pu). As observed, in most of the cases the double sequence method is
performing better regarding minimizing cost of asymmetrical fault to the grid, and
improving grid support.
149
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
Fig. 7.5 Comparison of cost for each control methods for each fault type.
7.3 Conclusion
In this chapter, alternative to CM, the dual-sequence (DS) method, which is realizing
voltage control in both positive and negative sequences, is given and shown to solve
adverse effects caused by CM. DS method is boosting only the faulted phases and
balancing the grid voltages.
As a general conclusion it can be commented that, with the use of DS method WPP can
mimic behaviour of CPP during asymmetrical faults, boosting the positive sequence
voltage and attenuating the negative sequence voltage, which results in improved grid
support.
150
Chapter 7 Control Solutions for Asymmetrical Faults
151
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
Chapter 8
Multi-Turbine Case Studies
In this chapter, the proposed control method given in chapter 5, namely PLL frequency
based current injection during severe symmetrical faults is simulated with a WPP
model of several wind turbines. The occurrence of the LOS problem and the interaction
of parallel connected WTs are investigated.
8.1 LOS Problem for Multi-Turbine Case
The structure of a generic WPP, which is aggregated as a single WT, has been given in
figure 1.1 and figure 2.2 and utilized throughout the thesis. In this chapter, the above
mentioned WPP, which is composed of 20 WTs of each 5MW ratings, is remodeled as
shown in figure 8.1 below. In this case one of the strings is expanded without
aggregation as 5 WTs and the rest is still kept as aggregated as 75MW. The PCC of the
WPP is again connected to the main grid via a 20km line, which has impedance of
0.1pu with X/R of 4; and the main grid is represented with its Thevenin equivalent with
impedance of 0.1pu and X/R of 10 (SCR is 10). The individual WTs in the expanded
string are connected with 500m long underground cables.
The purpose of the multi-turbine case is to observe the LOS conditions when the WTs
are operating in parallel and injecting active and reactive currents during faults, which
is occurring in real WPPs. As discussed in the previous chapters, LOS is occurring
when the current injection from the WPP is out of current transfer limits. For a detailed
WPP, the current injected into the grid is the combination of the individual currents
from each WT. Hence, the LOS can occur when the total current injection is out of the
current transfer limits; however each turbine experiences the LOS individually.
152
Chapter 8 Multi-Turbine Case Studies
Fig. 8.1 WPP diagram with an expanded string and Thevenin equivalent grid of
simulation study.
In order to observe that the parallel connected WTs can respond to the faults without
problems, a non-severe fault case is simulated first, where the PCC voltage drops to
25% of the rated. As seen in the second to fifth subfigures in figure 8.2, all the WTs
can inject active and reactive currents during fault, and can recover to normal operation
after the fault is cleared. In the sixth subfigure, the phase angles of the voltage at the
terminals of the aggregated WTs (WT-0), the five individual WTs (WT-1 to WT-5) and
the PCC are shown. Due to the resistive fault impedance, a phase jump is observed
when the fault is occurring at time is equal to 1 second. The frequency signals of the six
WTs (aggregated and individuals) are shown in the last subfigure, where it is observed
that all of the turbines stay synchronized at 50 Hz during the fault.
In figure 8.3, a result of a severe symmetrical fault, where the PCC voltage drops down
to 2% of the rated is shown. In this case, the WTs are having 1pu pure reactive current
references in accordance with the conventional method. As expected, the LOS occurs
and all of the WTs experience frequency deviation as fall towards 0 Hz, as observed in
the last subfigure. It is important to note that, since the impedance of 500m and 2km
long underground cable between the WTs is very small compared to the WPP
153
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
transformer impedance and 20km connection line, all the WTs operate almost
synchronous to each other having almost the same phase angle characteristics.
If the WPP was consisting of long collector grid between strings, considerable phase
differences would occur and LOS would be observed only for some of the WTs in the
1.5
1
0.5
0
0.9
1
1.1
1.2
1.3
1.4
1.5
1
0.5
0
0.9
1
1.1
1.2
1.3
1.4
-1
0.9
1
1.1
1.2
1.3
1.4
1.5
1
0.5
0
0.9
1
1.1
1.2
1.3
1.4
1
1.1
1.2
1.3
1.4
1
1.1
1.2
1.3
1.4
1
1.1
1.2
1.3
1.4
1
0
2
frequency (Hz)
Phase (degrees)
Iq-meas (pu)
Iq-ref (pu)
Id-meas (pu)
Id-ref (pu)
Vpcc (pu)
WPP.
1
0
0.9
200
0
-200
0.9
100
50
0
0.9
time (s)
Fig. 8.2 Non-severe fault case and support from the WPP (1) PCC bus voltage
magnitude, (2) Active current reference values, (3) Active current measured values (4)
Reactive current reference values (5) Reactive current measured values (6) Phase
angles (7) PLL frequency signals; WT-0: black, WT-1: blue, WT-2: yellow, WT-3:
green, WT-4: magenta, WT-5: red.
154
Chapter 8 Multi-Turbine Case Studies
1.5
1
0.5
0
0.9
1
1.1
1.2
1.3
1.4
1.5
1
0.5
0
0.9
1
1.1
1.2
1.3
1.4
-1
0.9
1
1.1
1.2
1.3
1.4
1.5
1
0.5
0
0.9
1
1.1
1.2
1.3
1.4
1
1.1
1.2
1.3
1.4
1
1.1
1.2
1.3
1.4
1
1.1
1.2
1.3
1.4
1
0
frequency (Hz)
Phase (degrees)
Iq-meas (pu)
Iq-ref (pu)
Id-meas (pu)
Id-ref (pu)
Vpcc (pu)
2
1
0
0.9
200
0
-200
0.9
100
50
0
0.9
time (s)
Fig. 8.3 Severe fault case and the LOS problem (1) PCC bus voltage magnitude, (2)
Active current reference values, (3) Active current measured values (4) Reactive
current reference values (5) Reactive current measured values (6) Phase angles (7) PLL
frequency signals; WT-0: black, WT-1: blue, WT-2: yellow, WT-3: green, WT-4:
magenta, WT-5: red.
8.2 PLL Frequency Based Solution for Multi-Turbine Case
In figure 8.4, the proposed PLL frequency based active current injection algorithm is
employed by all of the WTs in the WPP for the severe symmetrical fault case, which
was causing LOS in the previous section. As observed in the second and third
155
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
subfigures, all the WPPs generate active current setpoints around 0.4pu by the PLL
frequency based method. Since the WT capacity is limited to 1pu, the reactive current
references are decreased to less than 1pu in order to be able to inject the necessary
active current. As observed in the sixth and seventh subfigures, all of the WTs stay
1.5
1
0.5
0
0.9
1
1.1
1.2
1.3
1.4
1.5
1
0.5
0
0.9
1
1.1
1.2
1.3
1.4
-1
0.9
1
1.1
1.2
1.3
1.4
1.5
1
0.5
0
0.9
1
1.1
1.2
1.3
1.4
1
1.1
1.2
1.3
1.4
1
1.1
1.2
1.3
1.4
1
1.1
1.2
1.3
1.4
1
0
frequency (Hz)
Phase (degrees)
Iq-meas (pu)
Iq-ref (pu)
Id-meas (pu)
Id-ref (pu)
Vpcc (pu)
synchronized to the grid fundamental frequency.
2
1
0
0.9
200
0
-200
0.9
100
50
0
0.9
time (s)
Fig. 8.4 Severe fault case and the PLL frequency based solution (1) PCC bus voltage
magnitude, (2) Active current reference values, (3) Active current measured values (4)
Reactive current reference values (5) Reactive current measured values (6) Phase
angles (7) PLL frequency signals; WT-0: black, WT-1: blue, WT-2: yellow, WT-3:
green, WT-4: magenta, WT-5: red.
156
Chapter 8 Multi-Turbine Case Studies
8.3 Interaction between Wind Turbines
In figure 8.5, the severe symmetrical fault, which was causing LOS and shown to be
solved by the PLL frequency based method, is simulated again. However, in this case,
the 75MW part (WT-0) of the WPP is employing the conventional method and
injecting 1pu pure reactive current and the other 25MW (5 WTs) are employing the
1.5
1
0.5
0
0.9
1
1.1
1.2
1.3
1.4
1.5
1
0.5
0
0.9
1
1.1
1.2
1.3
1.4
-1
0.9
1
1.1
1.2
1.3
1.4
1.5
1
0.5
0
0.9
1
1.1
1.2
1.3
1.4
1
1.1
1.2
1.3
1.4
1
1.1
1.2
1.3
1.4
1
1.1
1.2
1.3
1.4
1
0
frequency (Hz)
Phase (degrees)
Iq-meas (pu)
Iq-ref (pu)
Id-meas (pu)
Id-ref (pu)
Vpcc (pu)
PLL frequency based method.
2
1
0
0.9
200
0
-200
0.9
100
50
0
0.9
time (s)
Fig. 8.5 Severe fault and interaction between WTs inside the WPP (1) PCC bus voltage
magnitude, (2) Active current reference values, (3) Active current measured values (4)
Reactive current reference values (5) Reactive current measured values (6) Phase
157
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
angles (7) PLL frequency signals; WT-0: black, WT-1: blue, WT-2: yellow, WT-3:
green, WT-4: magenta, WT-5: red.
As observed in the fourth and fifth subfigure, the WT-0 (75MW) is injecting 1pu
reactive current; and as observed in the second and third subfigure the 5 individual
WTs are injecting 0.7pu active current, which is required to compensate for the active
losses on the impedance between WTs and the faulted point. As observed in the fourth
and fifth subfigures, the 5 WTs are supplying the necessary amount of active current
while compromising their reactive current injection, which decreases to less than 1pu.
As observed in the sixth and seventh, with the PLL frequency based method, the WPP
can stay synchronized to the grid fundamental frequency, even though the majority of
the WPP do not contribute to the stability solution.
In the above case the WTs with PLL frequency based current injection method is
avoiding the LOS to occur for the whole WPP, including the other WTs. The above
mentioned interaction can also occur between neighboring WPPs; in case two WPPs
are connected to the same bus and a fault remote from that bus occurs, each WPP can
interact in a manner that the WPP with non-transferrable current references can cause
both itself and the other WPP to experience LOS, though the other WPP has current
references within current transfer limits. Hence the LOS situation can be triggered by
the neighboring power plants, whereas it can also be avoided by the neighboring power
plant.
158
Chapter 8 Multi-Turbine Case Studies
159
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
Chapter 9
Conclusions and Future Work
In this chapter, conclusions drawn from the thesis and main contributions are listed,
together with the future work.
9.1 Summary
As more renewable energy sources, especially wind power plants, are installed in the
power system, concern about stability of the power system increases. In order to
provide stable power system operation with high share of wind power, grid codes are
enforced by the transmission system operators of countries worldwide. Common to
most of the grid codes as a fundamental requirement, wind turbines are expected to stay
connected and inject reactive currents during grid faults. In certain grid codes, wind
turbines are required to inject positive sequence reactive currents even for severe
symmetrical faults with zero grid voltage; and also asymmetrical grid faults.
In this thesis, it is shown that during current injection to severe symmetrical faults with
very low (e.g. 5%) grid voltage, wind turbines are experiencing stability problem as
Loss of Synchronism (LOS) from grid fundamental frequency. The LOS is proven to
be related with active and reactive current transfer limits, which is a basic physical fact
not considered in wind power studies before, and derived within this thesis. It is shown
that active and reactive current references out of current transfer limits are driving the
grid synchronization (PLL) function of the wind turbines to large signal instability,
causing LOS. A novel algorithm, namely PLL frequency based current reference
generation, is proposed in this thesis as a solution for LOS. Both the LOS problem and
160
Chapter 9 Conclusions and Future Work
PLL frequency based solution are verified with time-domain simulations and gridconnected experiments.
Regarding the asymmetrical faults, it is shown that when pure positive sequence
reactive current is injected in accordance with the grid code requirements, positive
sequence grid voltage is boosted as desired, but negative sequence voltage is also
boosted, which is not desired considering unbalanced voltages. This coupling between
positive, negative and also zero sequence networks is explored for the first time in this
thesis. It is also shown that, pure positive sequence reactive current injection is causing
higher negative sequence voltages and higher phase overvoltages towards the WPPs.
As alternative to conventional method of pure positive sequence reactive current
injection, Dual-Sequence current injection method is given, which injects both positive
and negative sequence currents such that boosting and balancing the grid.
In summary, response of wind turbines complying with fault ride-through and reactive
current injection requirements of grid codes during severe symmetrical faults and
asymmetrical faults is investigated. In order to solve the observed problems and to
provide stable operation and improved grid support by wind turbines during
symmetrical and asymmetrical grid faults, new methods to generate active reactive
current references in positive and negative sequences are proposed to make the wind
turbines behave in a similar manner to conventional power plants.
Based on the observations, it can be commented that the fault ride-through requirement
together with the dynamic step response requirement of reactive current injection is
causing problems for wind power plants during severe faults, which can be solved with
advanced methods as given in this thesis. These requirements should be re-considered
in this manner, and suggestions or modifications should be included within grid codes.
Additionally, it can be commented that the grid code requirements for asymmetrical
faults have to be revised considering the impact of wind power plants’ current injection
on grid voltages and detailed specifications should be provided within grid codes.
161
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
Analysis of conventional synchronous generator’s response to grid faults is a mature
topic in classical power system literature. On the other hand, modern wind turbines
employ power electronics based converters, which employ control algorithms to inject
active and reactive currents. Hence, grid fault is a critical topic, where the classical
power systems and power electronics areas are intersecting. Thus, studies both on the
assessment of the grid code requirements and control solutions to satisfy grid code
requirements are needed in order to provide stable power system operation.
9.2 Main contributions
Main contributions of this thesis are listed below;
o
It is shown that similar to the active and reactive power transfer limits in classical
power system theory, active and reactive current transfer limits between two buses
exist for wind turbines’ current injection. These limits are derived for the first
time in this thesis as a fundamental theory to be utilized for specification of
current injection limits of wind turbines, and any other current-controlled gridconnected converter.
o
Wind turbines’ Loss of Synchronism (LOS) problem, which is occurring during
current injection to severe (very low voltage) symmetrical grid faults, is explored;
such that a physical fact, which has been omitted or not well-understood before, is
disclosed with its theory and analysis.
o
A novel wind turbine control method, PLL frequency based current reference
generation, is proposed for to solve LOS problem during severe symmetrical
faults.
o
Importance of fault impedance modeling in symmetrical and asymmetrical fault
analysis is explained, which gives insight for modeling and simulation studies.
o
Impact of coupling between positive, negative and zero sequence networks during
current injection of wind turbines to asymmetrical grid faults is explored and
analyzed, which has not been considered before.
o
Rise of negative sequence and non-faulty phase overvoltages are shown and
analyzed in detail when positive sequence reactive current is injected by wind
turbines in accordance with the grid code requirement.
162
Chapter 9 Conclusions and Future Work
o
Both for symmetrical and asymmetrical faults, understanding and knowledge is
provided, which would influence development of new grid codes for wind power
integration.
9.3 Future work
Following up the studies and investigations carried out in this thesis, the future work is
summarized in this section as below;
In chapter 2 and 4, it is shown that the wind turbines experience frequency deviation
and loss of vector control during an LOS event. In some cases, depending on the
duration of the fault and other parameters affecting the LOS event, the wind turbines
cannot recover their normal operation even though the fault is cleared. This
phenomenon is similar to the “rotor angle stability” of a synchronous generator. Hence,
together with a mathematical model and also incorporating the current regulator
dynamic bandwidth, a methodology similar to “equal area criteria” of classical power
system theory can be developed to analyze whether the wind turbine can recover (resynchronize) to the grid, based on the duration of the fault. Otherwise, several timedomain simulations can be run to analyze fault response of the wind turbine regarding
the fault duration and LOS; as done for synchronous generators to reach critical
clearing time.
The current transfer limits in chapter 3 and proposed PLL frequency based control in
chapter 5 have been studied for an aggregated wind power plant, and the model for
stability analysis is prepared for the same. A methodology can be created to analyze the
current transfer limits and LOS response of multi-turbines comprising a WPP.
Additionally, any elements like STATCOM, located within the WPP and any
(conventional) generators or loads located nearby PCC of the WPP can be included in
the methodology.
The frequency compensator of PLL frequency based control is designed as a
proportional control based on small-signal model of the PLL. An improved analysis
163
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
and design can be accomplished for proportional plus integral plus derivative control,
in order to achieve higher dynamic response during severe symmetrical faults.
Current injection by wind turbines during asymmetrical faults should be assessed from
protection point of view. Positive and negative sequence current injection and resulting
phase currents should be analyzed regarding their interaction with protection units (e.g.
relay settings) to observe if any improvement or degradation occurs. Additionally,
analysis of power system with high share of renewable energy sources should be
accomplished in order to observe effect of current injection on the phase overvoltages
and any other consequences during asymmetrical grid faults. WPP level control,
incorporating positive and negative sequence voltage management at the PCC point,
can be considered as a future asymmetrical fault handling solution.
As discussed in the previous sections, the problems are proposed to be solved by
generating active and reactive current references, which resulted in a WPP operation in
a similar manner to a synchronous generator. The proposed methods and alternatives
can be developed via utilizing advanced techniques and modern infrastructure of the
contemporary power system, such as wide area measurement systems and distributed
phase measurement units.
9.4 List of publications
P1. Mufit Altin, Ömer Göksu, Remus Teodorescu, Pedro Rodriguez, Birgitte BakJensen, and Lars Helle, “Overview of recent grid codes for wind power
integration,” International Conference on Optimization of Electrical and Electronic
Equipments, Romania, May 2010
P2. Ömer Göksu, Remus Teodorescu, Pedro Rodriguez, and Lars Helle, “A Review of
the State of the Art in Control of Variable-Speed Wind Turbines,” 9th International
Workshop on Large-Scale Integration of Wind Power into Power systems, Quebec,
Canada, October 2010
164
Chapter 9 Conclusions and Future Work
P3. Andrzej Adamczyk, Mufit Altin, Ömer Göksu, Remus Teodorescu, and Florin Iov,
“Generic 12-Bus Test System for Wind Power Integration Studies,” EPE Joint
Wind Energy and T&D Chapters Seminar, Aalborg, Denmark, June 2012
P4. Ömer Göksu, Remus Teodorescu, Birgitte Bak-Jensen, Florin Iov, and Philip Kjær,
"An Iterative Approach for Symmetrical and Asymmetrical Short-Circuit
Calculations with Converter-Based Connected Renewable Energy Sources.
Application to Wind Power," IEEE Power & Energy Society General Meeting, San
Diego, USA, July 2012
P5. Ömer Göksu, Remus Teodorescu, Claus Leth Bak, Florin Iov, and Philip Kjær,
"Impact of Wind Power Plant Reactive Current Injection during Asymmetrical
Grid Faults,” IET Journal of Renewable Power Generation, accepted.
P6. Ömer Göksu, Remus Teodorescu, Claus Leth Bak, Florin Iov, and Philip Kjær,
"Instability of Wind Turbine Converters during Current Injection to Low Voltage
Grid Faults and PLL Frequency Based Stability Solution,” IEEE Transactions on
Power Systems, under review.
165
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
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